Welcome to my detailed and comprehensive geodesic domes notes, actually the 2nd version (total rewrite of the 1st version). Since it has become so long I include a table of content ahead.

Table of Content

Changes

Introduction

Overview of Variants

How to Use the Notes

Strut Options & Notion

The Icosahedron

The Octahedron

The Cube

The Cuboctahedron

The Truncated Octahedron

The Rhombicuboctahedron

Building Models

Real Life Application

Links

Following changes were made to previous versions:

2nd version: Icosahedron, Octahedron, Cube, Cuboctahedron and Truncated Octahedron for each 1V to 6V or more triangulations, a few strut cutting optimization included. Be aware the notion of the strut types of Icosahedron 2V, 3V and 4V changed from previous version of the notes.
1st version: Icosahedron based domes covered in details: 2V, 3V and 4V with optimizations of cutting struts

If you don't care about the origin, the notion, the mathematics behind the geodesic domes, skip right to the 3rd page.

Construction of a planetarium of Carl Zeiss in Jena (Germany) 1922, planned by Walther Bauersfeld

Geodesic: from geodesy "surveying"; greek geodaisia "division of the earth"; geo "earth, land" + daiein "divide" - so far Buckminster Fuller 's often used notion, but as pointed out before, Walther Bauersfeld

created a "geodesic" dome in 1922 for Carl Zeiss in Jena (Germany), he even patented it in Germany 1925 (Patent Nr. 415395) as seen in this page

, so well over 20 years before B. Fuller was developing the "geodesic" approach.

The term "geodesic" is a mathematical term, which was adapted by Fuller to describe his approach, the term otherwise literally means "shortest path of two points on a sphere or curved space".

It seems Fuller simply wasn't aware of Bauersfeld prior work at Carl Zeiss, and reinvented and popularized it then in his life (1895 - 1983) and beyond via the Buckminster Fuller Institute these days.

US Pavilion at the Expo 1967 in Montreal (Canada) by Buckminster Fuller & Shoji Sadao
I discovered the geodesic dome first through DesertDomes.com web-site by Tara Landry and her dome calculator. The first version of my notes used the strut or chord factors she extracted from books by Hugh Kenner (Geodesic Math & How To Use It) and Lloyd Khan (Domebook I & II), who themselves relied on Fuller's work.

As a result of my study on geodesic polyhedra I wrote my own software tools to calculate, adjust and render 3D solids, such as platonic, archimedean and johnson solids, also generally known as regular and semi-regular polyhedra.

Based on that study of the manifold solids and their geodesic derivates I rewrote my "Geodesic Domes Notes" entirely with more variants (not just Icosahedron based domes) including dedicated calculators for each variant, optimization of cutting respective struts and a 2D construction map. And as the time goes by I will add more comments on each featured dome variant.

Icosahedron

Icosahedron 2ν (pre-normalized)

Icosahedron 2ν

Triangulate Methods
The procedure I feature as "geodesize" is to triangulate a triangle, or a polygon previously triangulated, and then normalize so the vector length is 1, this is also called spherized or spherical projected, as the point is forced to lie on the surface of a sphere.

To triangulate a triangle there are different methods or classes available, most prominent are the class 1 or alternate, and class 2 or triacon; additionally several "methods" are distincted - read for more at the References, in particular Joseph D. Clinton's work for NASA.

Of course you can also subdivide into other than triangles, such as other polygonal forms. I focus as a first step on the triangulation and its "class 1" or "alternate" way.

I have summarized several procedures incl. ones I discovered (some may have been used by others previously, I'm personally just not aware of it):

Buckminster Fuller introduced the notion of nν often also written as nV (V like in "vision", whereas ν is the greek letter "nu"), it means the amount of division of an original triangle. In this case the class 1 or alternate method is used, and from the original triangle.

Formulas:

n_t = n²

Example:

5V or 5ν has 5² triangles per original triangle

More in an accident I "geodesized" an already geodesized solid, because the program I wrote could not make subdivisions other than 2 at first, so in order to create 4V I thought to pipe it into the same program twice - and as a surprise the strut lengths varied from the 4V notion - I also came up with 5 strut lengths and not 6 as common for the 4V.

I realized then, the triangles were more even, smaller variance of strut lengths. In order to distinct this method from the nV notion I called it Level 1 or L1 and then L2. In order to make it more aligned with the nV notion: 1V and L1 are the same, 2V and L2 are also the same, but 4V and L3 differ then.

Formulas:

n_t = (2^(n-1))² = 2^2(n-1)

Example:

L5 = (2^5-1)² = 2^2(5-1) = 256 triangles per triangle

While I discovered a geodesized geodesize solid (like L3) provides different strut lengths and variance than a comperable, in sense of amount of subdivisions nV variant, I extended that it wouldn't necessary be the 2V to derive others, so I introduce the n₀V.n₁V . . . notion, concate the procedure of geodesize with '.' together.

2V.2V ~ 4V
3V.2V ~ 6V
2V.2V.2V ~ 8V

Formulas:

n_t = n₀² * n₁² * n₂² ...

Example:

2V.3V.2V ~ 12V = 2² * 3² * 2² = 144 triangles per original triangle

Just for sake of completeness:

L1 = 1V = 1V.1V
L2 = 2V = 2V¹ = L1.2V
L3 = 2V.2V = 2V² = L2.2V
L4 = 2V.2V.2V = 2V³ = L3.2V
L5 = 2V.2V.2V.2V = 2V⁴ = L4.2V

and also:
2V.2V != 4V but ~ 4V
3V.2V.2V != 12V but ~ 12V
L3 != 4V but ~ 4V
L4 != 8V but ~ 8V

Notions: '=' is equal, '!=' is not equal and '~' stands for similar

In order to normalize, we need to determine the distance of each vertice (x,y,z) from the center or an origin (x_origin,y_origin,z_origin):

d = √(x² + y² + z²)

or more general

d = √((x - x_origin)² + (y - y_origin)² + (z - z_origin)²)

To normalize we divide each of x, y and z by the distance:

x = x / d
y = y / d
z = z / d

or more general

x = (x - x_origin) / d + x_origin
y = (y - y_origin) / d + y_origin
z = (z - z_origin) / d + z_origin

which adjusts the point to have distance of 1 to the center - a sphere is a form where all points of the surface have the same distance to its center; so by normalizing the point is spherized or spherical projected.

There is far more math to cover in geodesic approaches, but for now I leave it at this and may extend it later more. A bit more math comes when calculating details of the required struts to compose a dome, this follows on the next page then.

NASA Contractor Report: Advanced Structural Geometry Studies, Part I: Polyhedral Subdivision Concepts for Structural Applications by Joseph D. Clinton (1971)
Geodesic Math by Joseph D. Clinton, rewrite by Jay Salsburg
Structural Design Concepts for Future Space Missions or "Geodesic Design Concepts" for NASA in 1968, by various authors incl. B. Fuller, rewrite by Jay Salsburg
Mother Earth News: Where Domes Come From (1971)

The next pages go into the details of the geodesic domes variants.

Since the possibilities are so vast I have selected a couple of platonic and archimedean solids - as I previously studied in Geodesic Polyhedra - which seem reasonable for dome constructions, and created variants with up 1000 struts, and max 30 different strut lengths. So, these are the results:

1V 2/3
25 struts (1 kind)

2V
65 struts (2 kinds)

3V 4/9
120 struts (3 kinds)

3V 5/9
165 struts (3 kinds)

4V
250 struts (6 kinds)

L3
250 struts (5 kinds)

5V 7/15
350 struts (9 kinds)

5V 8/15
425 struts (9 kinds)

6V
555 struts (9 kinds)

2V.3V
555 struts (10 kinds)

7V 10/21
700 struts (15 kinds)

7V 11/21
805 struts (15 kinds)

8V
980 struts (19 kinds)

L4
980 struts (14 kinds)

1V
8 struts (1 kind)

2V
28 struts (2 kinds)

3V
60 struts (3 kinds)

4V
104 struts (6 kinds)

L3
104 struts (5 kinds)

L3 3/8
60 struts (5 kinds)

L3 5/8
144 struts (5 kinds)

5V
160 struts (9 kinds)

6V
228 struts (9 kinds)

2V.3V
228 struts (10 kinds)

3V.2V
228 struts (7 kinds)

7V
308 struts (16 kinds)

8V
400 struts (20 kinds)

L4
400 struts (15 kinds)

L4 7/16
308 struts (15 kinds)

L4 9/16
488 struts (15 kinds)

9V
504 struts (18 kinds)

3V.3V
504 struts (15 kinds)

10V
620 struts (30 kinds)

2V.5V
620 struts (28 kinds)

5V.2V
620 struts (24 kinds)

1V
21 struts (2 kinds)

2V
78 struts (4 kinds)

3V
171 struts (10 kinds)

4V
300 struts (14 kinds)

L3
300 struts (11 kinds)

5V
465 struts (21 kinds)

6V
666 struts (29 kinds)

2V.3V
666 struts (27 kinds)

3V.2V
666 struts (22 kinds)

7V
903 struts (42 kinds)

1V
27 struts (2 kinds)

2V
102 struts (5 kinds)

3V
225 struts (10 kinds)

4V
396 struts (18 kinds)

L3
396 struts (15 kinds)

5V
615 struts (28 kinds)

6V
882 struts (36 kinds)

2V.3V
882 struts (34 kinds)

3V.2V
882 struts (28 kinds)

1V
60 struts (4 kinds)

2V
228 struts (7 kinds)

3V
504 struts (15 kinds)

4V
888 struts (25 kinds)

L3
888 struts (19 kinds)

1V 3/8
40 struts (2 kinds)

1V 5/8
88 struts (2 kinds)

2V 3/8
152 struts (5 kinds)

2V 5/8
344 struts (5 kinds)

3V 3/8
336 struts (10 kinds)

3V 5/8
768 struts (10 kinds)

In order to assist to overview the options further, consider to study following table carefully, it's worth it.

Types: strut types or amount of different strut lengths, the lesser the better
Variance: strut variance, difference between longest and shortest strut, the lesser the better (more even triangles)
The L-variant is better than the comperable V-variant, in sense of strut variance and amount of different struts.

The list is sorted by the amount of struts, so you can choose how complex the dome should become.

Name	Connectors	Faces	Struts	Types	Variance
Octahedron 1V	5	4	8	1	0%
Cube 1V	10	12	21	2	25.6%
Icosahedron 1V 2/3	11	15	25	1	0%
Cuboctahedron 1V	12	16	27	2	30.7%
Octahedron 2V	13	16	28	2	30.7%
Rhombicuboctahedron 1V 3/8	17	24	40	2	36.5%
Octahedron 3V	25	36	60	3	46.1%
Octahedron L3 3/8	25	36	60	5	48.0%
Truncated Octahedron 1V	25	36	60	4	46.1%
Icosahedron 2V	26	40	65	2	13.1%
Cube 2V	31	48	78	4	37.4%
Rhombicuboctahedron 1V 5/8	33	56	88	2	36.5%
Name	Connectors	Faces	Struts	Types	Variance
Cuboctahedron 2V	39	64	102	5	48.0%
Octahedron 4V	41	64	104	6	80.2%
Octahedron L3	41	64	104	5	48.0%
Icosahedron 3V 4/9	46	75	120	3	18.3%
Octahedron L3 5/8	53	92	144	5	48.0%
Rhombicuboctahedron 2V 3/8	57	96	152	5	44.9%
Octahedron 5V	61	100	160	9	92.9%
Icosahedron 3V 5/9	61	105	165	3	18.3%
Cube 3V	64	108	171	10	50.1%
Cuboctahedron 3V	82	144	225	10	51.2%
Octahedron 2V.3V	85	144	228	10	51.2%
Octahedron 3V.2V	85	144	228	7	53.5%
Name	Connectors	Faces	Struts	Types	Variance
Octahedron 6V	85	144	228	9	95.4%
Truncated Octahedron 2V	85	144	228	7	53.5%
Icosahedron 4V	91	160	250	6	28.3%
Icosahedron L3	91	160	250	5	17.8%
Cube 4V	109	192	300	14	56.9%
Cube L3	109	192	300	11	41.5%
Octahedron 7V	113	196	308	16	107.9%
Octahedron L4 7/16	113	196	308	15	53.8%
Rhombicuboctahedron 3V 3/8	121	216	336	10	46.2%
Rhombicuboctahedron 2V 5/8	121	224	344	5	44.9%
Icosahedron 5V 7/15	126	225	350	9	32.1%
Cuboctahedron 4V	141	256	396	18	60.2%
Name	Connectors	Faces	Struts	Types	Variance
Cuboctahedron L3	141	256	396	15	53.8%
Octahedron 8V	145	256	400	20	112.6%
Octahedron L4	145	256	400	15	53.8%
Icosahedron 5V 8/15	151	275	425	9	32.1%
Cube 5V	166	300	465	21	58.9%
Octahedron L4 9/16	173	316	488	15	53.8%
Octahedron 3V.3V	181	324	504	15	55.1%
Octahedron 9V	181	324	504	18	113.2%
Truncated Octahedron 3V	181	324	504	15	55.1%
Icosahedron 2V.3V	196	360	555	10	18.9%
Icosahedron 6V	196	360	555	9	33.2%
Cuboctahedron 5V	216	400	615	28	62.8%
Name	Connectors	Faces	Struts	Types	Variance
Octahedron 10V	221	400	620	30	119.3%
Octahedron 2V.5V	221	400	620	28	62.8%
Octahedron 5V.2V	221	400	620	24	98.1%
Cube 2V.3V	235	432	666	27	44.4%
Cube 3V.2V	235	432	666	22	52.3%
Cube 6V	235	432	666	29	63.1%
Icosahedron 7V 10/21	246	455	700	15	36.5%
Rhombicuboctahedron 3V 5/8	265	504	768	10	46.2%
Icosahedron 7V 11/21	281	525	805	15	36.5%
Cuboctahedron 2V.3V	307	576	882	34	54.6%
Cuboctahedron 3V.2V	307	576	882	28	53.6%
Cuboctahedron 6V	307	576	882	36	63.1%
Name	Connectors	Faces	Struts	Types	Variance
Truncated Octahedron 4V	313	576	888	25	58.0%
Truncated Octahedron L3	313	576	888	19	55.6%
Cube 7V	316	588	903	42	64.0%
Icosahedron 8V	341	640	980	19	37.7%
Icosahedron L4	341	640	980	14	19.0%

Note: all strut lengths have been sorted by 1/10'000th or +/-0.00005 exact

Amount of Struts vs Strut Variance

Note: Click on the graphic, and click "full scale" or scroll down, and press "Print" link at the bottom of the page.

In the graphic you actually see why the Icosahedron looks best, it has the least strut variance, which is an indication of more or less similiar triangles through the entire structure. And as realized before, the Ln variants additionally provide better results than the nV counterparts. The Octahedron variants, on the other hand, have high strut variances as seen above.

I personally like the Cuboctahedron variants, but they have more strut variance than the Icosahedron, in other words, at the end it's your personal choice and favours which lead you to choose a polyhedral geodesic dome variant, the list above and this graphic may just assist you in your overall considerations.

Amount of Struts vs Strut Types

Note: Click on the graphic, and click "full scale" or scroll down, and press "Print" link at the bottom of the page.

In this graphic above the Icosahedron does quite well, with low amount of strut lengths, and again there also Ln provides better results than the nV variants. Interesting also the Rhombicuboctahedron comes with even lower amount of strut lengths than the Icosahedron.

The amount of different strut lengths has a direct impact on the construction, the lesser the amount of different strut lengths the better - as you have less cut optimization to calculate and therefore less waste to expect. So it's certainly an aspect to value when choosing a variant to build. As mentioned already, the struts are sorted in 1/10'000th and you may notice on the details of the variants on the following pages, that you can sum together near the same length struts in case you compose a smaller dome, e.g. < 8m or so. For large scale domes it may be crucial to remain as precise as you can and I leave it up to you to treat certain struts of alike length as the same or not.

I recommend you choose a dome variant you like to construct ...

look what base appeals to you most, as a first step disregard any other kind of argument
check the amount of different strut types, amount of struts itself - and become aware of the overall overhead (e.g. whether building an edgy 1V or 2V, or a smoother 4V or higher with far more struts)
how temporary shall the dome become? e.g. a 4V Icosahedron Dome skeleton with 250 struts I raise as a single person in 4-5 hours
the higher the subdivision the more exact you need to work, little difference will distort and weaken the construction

... and once you decided which variant(s) you consider more closely, then ...

print out that particular page of the dome variant with your settings - as the notes are subject of change, and may later not be available or available with a different notion
make a 10:1 or 20:1 sized model (e.g. 6m full scale dome, create a 0.60m model), it gives you a sense of the overhead, amount of struts, connectors etc
think about the kind of strut and its connectors you gonna use, e.g. metal, wood, plastic etc and make tests with the actual material, create a 5-way or 6-way connector construction and test its stability

For each dome variant there is a small calculator, to calculate diameter to the different struts, additionally the l_hole can be entered.

Notion of a dome strut (A vs A_lath) & l_hole

Timber based strut, metallic plate as connector, rather cheap with average labour.

Pipe Hub Closeup (courtesy by Michal Wielgus)
Timber based strut, with a steel pipe as connector, moderately cheap with average labour, prefereable for more lasting constructions.

Michal Wielgus who sent me the photo used this hub for a 3V 5/9 icosahedron based geodesic dome, he calculated the holes in the pipe for the 5- and 6-way simply by d_pipe π / 5 or 6, which was exact enough he said. For the 4-way connectors on the base require the same calculation as the 6-way, and leaving the two bottom directed connectors empty.

To be more precise each hub would require the angles according, A, B, C, etc ...

Following photos were kindly shared by Haan from Korea , who made a 2V icosahedron based geodesic dome, with 7m diameter, 11cm diameter steel pipe:

Haan's Dome (2v icosa, 7m diameter): 10cm thick wooden struts
2008/04/18 08:02

Haan's Dome (2v icosa, 7m diameter): drilling tool & anchor bolt
2008/04/18 11:53

Haan's Dome (2v icosa, 7m diameter): hub detail with steel pipe
2008/04/18 07:53

Haan's Dome (2v icosa, 7m diameter): hub detail with steel pipe
2008/04/18 07:58

Haan's Dome (2v icosa, 7m diameter): complete setup
2008/04/18 08:07

Steel/aluminium/etc tube or pipe, and ends squeezed, also rather cheap with little labour. This options is very popular using conduits. Desert Domes: Conduit Domes Tips has some useful information on this option.

Bamboo (different diameters) with soft-pipe as connector, very cheap but increased labour, and only suitable for small domes < 4-5m diameter and lower sub-division frequencies (e.g. 2V, 3V), e.g. for play domes.

Cut pointing ends
2007/02/14 11:47

4V Geodesic Dome (6.33m) (Closeup 1)
2007/03/16 15:53

Connector (Closeup)
2007/03/17 10:39

For temporary setups it's obvious to use struts which built-in connectors, e.g. endings which operate as connector.

CONBAM.de , german bamboo expert, has special connectors for more stable and large domes, with a large dome construction example.

Strut Angle α_strut
The angle α_strut can be calculated with a bit of trigonometry. α shall be the angle between the tangent (green in the illustration) and the strut:

h = √(r² - l_strut²/4)
h = r * cos(γ/2)
γ = 2 acos(h/r) = 2 acos(√(r² - l_strut²/4) / r)
α = 90-&beta
β = (180-γ)/2
α = 90 - (180-γ)/2 = γ/2
α = α_strut = acos(√(r² - l_strut²/4) / r)

finally α is also the angle to bend the endings α_strut. The following pages with all the variant details provides you for each strut the corresponding α_strut as well.

Hub/Strut Angles

In case you require the exact angles for the faces, e.g. for a pipe hub or for composing individual faces, according the SSS Theorem

, known all 3 sides of a triangle searching the angles, we can calculate all angles:

α = acos((B²+C²-A²)/(2 B C))
β = acos((A²+C²-B²)/(2 A C))
γ = acos((A²+B²-C²)/(2 A B))

For now, all the faces are sorted and the angles are given for all variants. I may add later a list of hubs and their angles, but you can sort them your based on the construction maps.

Icosahedron

Uniform Polyhedron: U22
Platonic Solid
Platonic Element: Water
Vertices: 12
Edges: 30
Faces: 20
Wythoff symbol: 5|2 3
Symmetry Group: icosahedral
Vertex Configuration: {3, 3, 3, 3, 3}
Dual: dodecahedron
V: s³ * 5/12 * (3 + √5)
A: s² * 20 / 4 * √3
r_inner: s / 12 * (3 * √3 + √15)
r_outer: s / 4 * √(10 + 2 * √5)

Geodesic 1V 2/3 Icosahedron Dome (front view)

Geodesic 1V 2/3 Icosahedron Dome (bird view)

vertices/connectors: 11
- 5 x 4-way
- 6 x 5-way
1V 2/3 Icosahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 25: 1.05146 (31.72°)
faces: 15 (3-sided)
- A-A-A x 15 (60.00°, 60.00°, 60.00°)
diameter: 2.000, radius: 1.000
height: 1.447 or 72.36% of diameter

Geodesic 1V 2/3 Icosahedron Dome (Human is 170cm/5'7")

Geodesic 2V Icosahedron Dome (front view)

Geodesic 2V Icosahedron Dome (bird view)

vertices/connectors: 26
- 10 x 4-way
- 6 x 5-way
- 10 x 6-way
2V Icosahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 30: 0.54653 (15.86°)
- B x 35: 0.61803 (18.00°)
- total 65 struts (2 kinds)¹⁾
- strut variance 13.1%
faces: 40 (3-sided)
- A-A-B x 30 (55.57°, 55.57°, 68.86°)
- B-B-B x 10 (60.00°, 60.00°, 60.00°)
- 2 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 2V Icosahedron Dome (Human is 170cm/5'7")

In some literature this variant is also called "3V 3/8 Dome".

Geodesic 3V 4/9 Icosahedron Dome (front view)

Geodesic 3V 4/9 Icosahedron Dome (bird view)

vertices/connectors: 46
- 15 x 4-way
- 6 x 5-way
- 25 x 6-way
3V 4/9 Icosahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 30: 0.34862 (10.04°)
- B x 40: 0.40355 (11.64°)
- C x 50: 0.41241 (11.90°)
- total 120 struts (3 kinds)¹⁾
- strut variance 18.3%
faces: 75 (3-sided)
- A-A-B x 30 (54.63°, 54.63°, 70.74°)
- B-C-C x 45 (58.59°, 60.70°, 60.70°)
- 2 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 0.828 or 41.42% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 3V 4/9 Icosahedron Dome (Human is 170cm/5'7")

As you see the bottom isn't entirely even, for heavy construction you have to level them.
In some literature this variant is also called "3V 5/8 Dome".

Geodesic 3V 5/9 Icosahedron Dome (front view)

Geodesic 3V 5/9 Icosahedron Dome (bird view)

vertices/connectors: 61
- 15 x 4-way
- 6 x 5-way
- 40 x 6-way
3V 5/9 Icosahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 30: 0.34862 (10.04°)
- B x 55: 0.40355 (11.64°)
- C x 80: 0.41241 (11.90°)
- total 165 struts (3 kinds)¹⁾
- strut variance 18.3%
faces: 105 (3-sided)
- A-A-B x 30 (54.63°, 54.63°, 70.74°)
- B-C-C x 75 (58.59°, 60.70°, 60.70°)
- 2 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.188 or 59.38% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 3V 5/9 Icosahedron Dome (Human is 170cm/5'7")

As you see here as well that the bottom isn't entirely even, for heavy construction you have to level them.

Geodesic 4V Icosahedron Dome (front view)

Geodesic 4V Icosahedron Dome (bird view)

vertices/connectors: 91
- 20 x 4-way
- 6 x 5-way
- 65 x 6-way
4V Icosahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 30: 0.25318 (7.27°)
- B x 60: 0.29453 (8.47°)
- C x 30: 0.29524 (8.49°)
- D x 30: 0.29859 (8.59°)
- E x 70: 0.31287 (9.00°)
- F x 30: 0.32492 (9.35°)
- total 250 struts (6 kinds)¹⁾
- strut variance 28.3%
faces: 160 (3-sided)
- A-A-C x 30 (54.34°, 54.34°, 71.32°)
- B-B-C x 30 (59.92°, 59.92°, 60.16°)
- B-D-E x 60 (57.52°, 58.80°, 63.68°)
- E-E-F x 30 (58.72°, 58.72°, 62.55°)
- F-F-F x 10 (60.00°, 60.00°, 60.00°)
- 5 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 4V Icosahedron Dome (Human is 170cm/5'7")

The 4V looks very attractive, yet, I would recommend using the L3 version instead with less strut lengths and less strut variance.

Geodesic L3 Icosahedron Dome (front view)

Geodesic L3 Icosahedron Dome (bird view)

vertices/connectors: 91
- 20 x 4-way
- 6 x 5-way
- 65 x 6-way
L3 Icosahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 60: 0.27590 (7.93°)
- B x 60: 0.28547 (8.21°)
- C x 70: 0.31287 (9.00°)
- D x 30: 0.32124 (9.24°)
- E x 30: 0.32492 (9.35°)
- total 250 struts (5 kinds)¹⁾
- strut variance 17.8%
faces: 160 (3-sided)
- A-A-D x 30 (54.40°, 54.40°, 71.20°)
- A-B-C x 60 (54.68°, 57.60°, 67.72°)
- B-B-D x 30 (55.77°, 55.77°, 68.46°)
- C-C-E x 30 (58.72°, 58.72°, 62.55°)
- E-E-E x 10 (60.00°, 60.00°, 60.00°)
- 5 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic L3 Icosahedron Dome (Human is 170cm/5'7")

The L3 might be a better choice for a 250 strut dome than the 4V variant: the L3 provides less strut variance 17.8% (5 kinds of struts) instead of 28.3% (6 kinds of struts).

Geodesic 5V 7/15 Icosahedron Dome (front view)

Geodesic 5V 7/15 Icosahedron Dome (bird view)

vertices/connectors: 126
- 25 x 4-way
- 6 x 5-way
- 95 x 6-way
5V 7/15 Icosahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 30: 0.19815 (5.69°)
- B x 60: 0.22569 (6.48°)
- C x 30: 0.23160 (6.65°)
- D x 30: 0.23179 (6.66°)
- E x 50: 0.24509 (7.04°)
- F x 10: 0.24535 (7.05°)
- G x 60: 0.24724 (7.10°)
- H x 50: 0.25517 (7.33°)
- I x 30: 0.26160 (7.52°)
- total 350 struts (9 kinds)¹⁾
- strut variance 32.1%
faces: 225 (3-sided)
- A-A-D x 30 (54.19°, 54.19°, 71.61°)
- B-B-D x 30 (59.10°, 59.10°, 61.80°)
- B-C-G x 60 (56.13°, 58.44°, 65.43°)
- E-E-F x 20 (59.96°, 59.96°, 60.08°)
- E-G-H x 50 (58.37°, 59.18°, 62.45°)
- H-H-I x 25 (59.17°, 59.17°, 61.67°)
- I-I-I x 10 (60.00°, 60.00°, 60.00°)
- 7 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 0.896 or 44.78% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 5V 7/15 Icosahedron Dome (Human is 170cm/5'7")

Geodesic 5V 8/15 Icosahedron Dome (front view)

Geodesic 5V 8/15 Icosahedron Dome (bird view)

vertices/connectors: 151
- 25 x 4-way
- 6 x 5-way
- 120 x 6-way
5V 8/15 Icosahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 30: 0.19815 (5.69°)
- B x 60: 0.22569 (6.48°)
- C x 30: 0.23160 (6.65°)
- D x 30: 0.23179 (6.66°)
- E x 80: 0.24509 (7.04°)
- F x 20: 0.24535 (7.05°)
- G x 70: 0.24724 (7.10°)
- H x 70: 0.25517 (7.33°)
- I x 35: 0.26160 (7.52°)
- total 425 struts (9 kinds)¹⁾
- strut variance 32.1%
faces: 275 (3-sided)
- A-A-D x 30 (54.19°, 54.19°, 71.61°)
- B-B-D x 30 (59.10°, 59.10°, 61.80°)
- B-C-G x 60 (56.13°, 58.44°, 65.43°)
- E-E-F x 40 (59.96°, 59.96°, 60.08°)
- E-G-H x 70 (58.37°, 59.18°, 62.45°)
- H-H-I x 35 (59.17°, 59.17°, 61.67°)
- I-I-I x 10 (60.00°, 60.00°, 60.00°)
- 7 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.111 or 55.56% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 5V 8/15 Icosahedron Dome (Human is 170cm/5'7")

Geodesic 6V Icosahedron Dome (front view)

Geodesic 6V Icosahedron Dome (bird view)

vertices/connectors: 196
- 30 x 4-way
- 6 x 5-way
- 160 x 6-way
6V Icosahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 30: 0.16257 (4.66°)
- B x 60: 0.18191 (5.22°)
- C x 30: 0.18738 (5.38°)
- D x 30: 0.19048 (5.47°)
- E x 60: 0.19801 (5.68°)
- F x 90: 0.20282 (5.82°)
- G x 130: 0.20591 (5.91°)
- H x 65: 0.21535 (6.18°)
- I x 60: 0.21663 (6.22°)
- total 555 struts (9 kinds)¹⁾
- strut variance 33.2%
faces: 360 (3-sided)
- A-A-D x 30 (54.14°, 54.14°, 71.72°)
- B-B-D x 30 (58.42°, 58.42°, 63.15°)
- B-C-F x 60 (55.40°, 58.00°, 66.60°)
- E-F-G x 120 (57.95°, 60.24°, 61.81°)
- G-G-H x 60 (58.46°, 58.46°, 63.08°)
- H-I-I x 60 (59.63°, 60.18°, 60.18°)
- 6 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 6V Icosahedron Dome (Human is 170cm/5'7")

Geodesic 2V.3V Icosahedron Dome (front view)

Geodesic 2V.3V Icosahedron Dome (bird view)

vertices/connectors: 196
- 30 x 4-way
- 6 x 5-way
- 160 x 6-way
2V.3V Icosahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 60: 0.18212 (5.22°)
- B x 30: 0.18854 (5.41°)
- C x 60: 0.18922 (5.43°)
- D x 60: 0.18932 (5.43°)
- E x 60: 0.19125 (5.49°)
- F x 70: 0.20591 (5.91°)
- G x 30: 0.21321 (6.12°)
- H x 60: 0.21445 (6.16°)
- I x 65: 0.21535 (6.18°)
- J x 60: 0.21663 (6.22°)
- total 555 struts (10 kinds)¹⁾
- strut variance 18.9%
faces: 360 (3-sided)
- A-A-G x 30 (54.17°, 54.17°, 71.66°)
- A-C-F x 60 (54.69°, 57.98°, 67.33°)
- B-D-H x 60 (55.23°, 55.58°, 69.19°)
- C-E-H x 60 (55.22°, 56.15°, 68.63°)
- D-D-G x 30 (55.73°, 55.73°, 68.54°)
- E-E-I x 30 (55.74°, 55.74°, 68.53°)
- F-F-I x 30 (58.46°, 58.46°, 63.08°)
- I-J-J x 60 (59.63°, 60.18°, 60.18°)
- 8 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 2V.3V Icosahedron Dome (Human is 170cm/5'7")

The 2V.3V has 10 kinds of strut lengths, and 18.7% strut variance - compared to 6V with 9 kinds and 33.3% variance. So, you might think about prefering more even triangles, choose 2V.3V or less struth kinds then the 6V.

The 3V.2V Icosahedron could also be used to achieve the same amount of subdivision, yet, the 3V is a bit uneven around the base, and the 2nd stage of 2V doesn't even this again, so the base isn't even, yet, 7 kinds of struts. I won't list the details as I won't recommend 3V.2V over 2V.3V or 6V at all.

Geodesic 7V 10/21 Icosahedron Dome (front view)

Geodesic 7V 10/21 Icosahedron Dome (bird view)

vertices/connectors: 246
- 35 x 4-way
- 6 x 5-way
- 205 x 6-way
7V 10/21 Icosahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 30: 0.13774 (3.95°)
- B x 60: 0.15197 (4.36°)
- C x 30: 0.15664 (4.49°)
- D x 30: 0.16154 (4.63°)
- E x 60: 0.16480 (4.73°)
- F x 30: 0.17066 (4.90°)
- G x 60: 0.17098 (4.90°)
- H x 60: 0.17132 (4.91°)
- I x 50: 0.17353 (4.98°)
- J x 70: 0.17585 (5.04°)
- K x 50: 0.18155 (5.21°)
- L x 30: 0.18161 (5.21°)
- M x 50: 0.18237 (5.23°)
- N x 60: 0.18548 (5.32°)
- O x 30: 0.18791 (5.39°)
- total 700 struts (15 kinds)¹⁾
- strut variance 36.5%
faces: 455 (3-sided)
- A-A-D x 30 (54.10°, 54.10°, 71.81°)
- B-B-D x 30 (57.91°, 57.91°, 64.18°)
- B-C-H x 60 (55.01°, 57.57°, 67.41°)
- E-F-J x 60 (56.76°, 60.03°, 63.21°)
- E-G-H x 60 (57.56°, 61.13°, 61.31°)
- G-G-L x 30 (57.93°, 57.93°, 64.15°)
- I-I-J x 20 (59.54°, 59.54°, 60.92°)
- I-J-M x 50 (57.89°, 59.18°, 62.93°)
- K-K-L x 25 (59.98°, 59.98°, 60.04°)
- K-M-N x 50 (59.11°, 59.59°, 61.29°)
- N-N-O x 30 (59.57°, 59.57°, 60.86°)
- O-O-O x 10 (60.00°, 60.00°, 60.00°)
- 12 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 0.925 or 46.26% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 7V 10/21 Icosahedron Dome (Human is 170cm/5'7")

Geodesic 7V 11/21 Icosahedron Dome (front view)

Geodesic 7V 11/21 Icosahedron Dome (bird view)

vertices/connectors: 281
- 35 x 4-way
- 6 x 5-way
- 240 x 6-way
7V 11/21 Icosahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 30: 0.13774 (3.95°)
- B x 60: 0.15197 (4.36°)
- C x 30: 0.15664 (4.49°)
- D x 30: 0.16154 (4.63°)
- E x 60: 0.16480 (4.73°)
- F x 30: 0.17066 (4.90°)
- G x 60: 0.17098 (4.90°)
- H x 60: 0.17132 (4.91°)
- I x 80: 0.17353 (4.98°)
- J x 90: 0.17585 (5.04°)
- K x 70: 0.18155 (5.21°)
- L x 35: 0.18161 (5.21°)
- M x 70: 0.18237 (5.23°)
- N x 70: 0.18548 (5.32°)
- O x 30: 0.18791 (5.39°)
- total 805 struts (15 kinds)¹⁾
- strut variance 36.5%
faces: 525 (3-sided)
- A-A-D x 30 (54.10°, 54.10°, 71.81°)
- B-B-D x 30 (57.91°, 57.91°, 64.18°)
- B-C-H x 60 (55.01°, 57.57°, 67.41°)
- E-F-J x 60 (56.76°, 60.03°, 63.21°)
- E-G-H x 60 (57.56°, 61.13°, 61.31°)
- G-G-L x 30 (57.93°, 57.93°, 64.15°)
- I-I-J x 40 (59.54°, 59.54°, 60.92°)
- I-J-M x 70 (57.89°, 59.18°, 62.93°)
- K-K-L x 35 (59.98°, 59.98°, 60.04°)
- K-M-N x 70 (59.11°, 59.59°, 61.29°)
- N-N-O x 30 (59.57°, 59.57°, 60.86°)
- O-O-O x 10 (60.00°, 60.00°, 60.00°)
- 12 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.080 or 54.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 7V 11/21 Icosahedron Dome (Human is 170cm/5'7")

Geodesic 8V Icosahedron Dome (front view)

Geodesic 8V Icosahedron Dome (bird view)

vertices/connectors: 341
- 40 x 4-way
- 6 x 5-way
- 295 x 6-way
8V Icosahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 30: 0.11946 (3.42°)
- B x 60: 0.13033 (3.74°)
- C x 30: 0.13424 (3.85°)
- D x 30: 0.14018 (4.02°)
- E x 60: 0.14056 (4.03°)
- F x 60: 0.14548 (4.17°)
- G x 30: 0.14628 (4.19°)
- H x 60: 0.14803 (4.24°)
- I x 60: 0.14862 (4.26°)
- J x 60: 0.15267 (4.38°)
- K x 70: 0.15296 (4.39°)
- L x 30: 0.15315 (4.39°)
- M x 60: 0.15477 (4.44°)
- N x 90: 0.15636 (4.48°)
- O x 60: 0.16033 (4.60°)
- P x 30: 0.16036 (4.60°)
- Q x 70: 0.16088 (4.61°)
- R x 60: 0.16300 (4.67°)
- S x 30: 0.16465 (4.72°)
- total 980 struts (19 kinds)¹⁾
- strut variance 37.7%
faces: 640 (3-sided)
- A-A-D x 30 (54.08°, 54.08°, 71.83°)
- B-B-D x 30 (57.45°, 57.45°, 65.09°)
- B-C-H x 60 (54.73°, 57.24°, 68.03°)
- E-F-H x 60 (57.24°, 60.49°, 62.28°)
- E-G-J x 60 (56.05°, 59.67°, 64.28°)
- F-F-N x 30 (57.49°, 57.49°, 65.02°)
- I-J-N x 60 (57.45°, 60.02°, 62.52°)
- I-K-L x 60 (58.06°, 60.90°, 61.04°)
- K-K-P x 30 (58.39°, 58.39°, 63.23°)
- M-M-N x 30 (59.66°, 59.66°, 60.69°)
- M-N-Q x 60 (58.38°, 59.36°, 62.26°)
- O-O-P x 30 (59.98°, 59.98°, 60.04°)
- O-Q-R x 60 (59.32°, 59.69°, 60.99°)
- R-R-S x 30 (59.67°, 59.67°, 60.65°)
- S-S-S x 10 (60.00°, 60.00°, 60.00°)
- 15 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 8V Icosahedron Dome (Human is 170cm/5'7")

Geodesic L4 Icosahedron Dome (front view)

Geodesic L4 Icosahedron Dome (bird view)

vertices/connectors: 341
- 40 x 4-way
- 6 x 5-way
- 295 x 6-way
L4 Icosahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 120: 0.13828 (3.96°)
- B x 120: 0.13951 (4.00°)
- C x 120: 0.14310 (4.10°)
- D x 60: 0.14429 (4.14°)
- E x 60: 0.14439 (4.14°)
- F x 140: 0.15692 (4.50°)
- G x 60: 0.15800 (4.53°)
- H x 60: 0.15846 (4.54°)
- I x 60: 0.16115 (4.62°)
- J x 30: 0.16217 (4.65°)
- K x 30: 0.16228 (4.65°)
- L x 60: 0.16300 (4.67°)
- M x 30: 0.16448 (4.72°)
- N x 30: 0.16465 (4.72°)
- total 980 struts (14 kinds)¹⁾
- strut variance 19.0%
faces: 640 (3-sided)
- A-A-J x 30 (54.10°, 54.10°, 71.80°)
- A-B-I x 60 (54.21°, 54.90°, 70.89°)
- A-C-G x 60 (54.41°, 57.29°, 68.29°)
- A-D-F x 60 (54.47°, 58.12°, 67.41°)
- B-B-J x 30 (54.45°, 54.45°, 71.09°)
- B-C-F x 60 (55.19°, 57.38°, 67.44°)
- B-D-G x 60 (54.74°, 57.63°, 67.64°)
- C-C-K x 30 (55.45°, 55.45°, 69.09°)
- C-E-I x 60 (55.54°, 56.30°, 68.16°)
- E-E-K x 30 (55.81°, 55.81°, 68.39°)
- F-F-M x 30 (58.38°, 58.38°, 63.23°)
- F-H-L x 60 (58.40°, 59.36°, 62.23°)
- H-H-M x 30 (58.74°, 58.74°, 62.52°)
- L-L-N x 30 (59.67°, 59.67°, 60.65°)
- N-N-N x 10 (60.00°, 60.00°, 60.00°)
- 15 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic L4 Icosahedron Dome (Human is 170cm/5'7")

Octahedron

Uniform Polyhedron: U5
Platonic Solid
Platonic Element: Air
Vertices: 6
Edges: 12
Faces: 8
Wythoff symbol: 4|2 3
Symmetry Group: octahedral
Vertex Configuration: {3, 3, 3, 3}
Dual: cube
V: s³ / 3 * √2
A: s² * 8 / 4 * √3
r_inner: s / 6 * √6
r_outer: s / 2 * √2

Geodesic 1V Octahedron Dome (front view)

Geodesic 1V Octahedron Dome (bird view)

vertices/connectors: 5
- 4 x 3-way
- 1 x 4-way
1V Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 8: 1.41421 (45.00°)
faces: 4 (3-sided)
- A-A-A x 4 (60.00°, 60.00°, 60.00°)
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

Geodesic 1V Octahedron Dome (Human is 170cm/5'7")

Geodesic 2V Octahedron Dome (front view)

Geodesic 2V Octahedron Dome (bird view)

vertices/connectors: 13
- 4 x 3-way
- 5 x 4-way
- 4 x 6-way
2V Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 16: 0.76537 (22.50°)
- B x 12: 1.00000 (30.00°)
- total 28 struts (2 kinds)¹⁾
- strut variance 30.7%
faces: 16 (3-sided)
- A-A-B x 12 (49.21°, 49.21°, 81.57°)
- B-B-B x 4 (60.00°, 60.00°, 60.00°)
- 2 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 2V Octahedron Dome (Human is 170cm/5'7")

Geodesic 3V Octahedron Dome (front view)

Geodesic 3V Octahedron Dome (bird view)

vertices/connectors: 25
- 4 x 3-way
- 9 x 4-way
- 12 x 6-way
3V Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 16: 0.45951 (13.28°)
- B x 20: 0.63246 (18.44°)
- C x 24: 0.67142 (19.62°)
- total 60 struts (3 kinds)¹⁾
- strut variance 46.1%
faces: 36 (3-sided)
- A-A-B x 12 (46.51°, 46.51°, 86.98°)
- B-C-C x 24 (56.20°, 61.90°, 61.90°)
- 2 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 3V Octahedron Dome (Human is 170cm/5'7")

Geodesic 4V Octahedron Dome (front view)

Geodesic 4V Octahedron Dome (bird view)

vertices/connectors: 41
- 4 x 3-way
- 13 x 4-way
- 24 x 6-way
4V Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 16: 0.32036 (9.22°)
- B x 24: 0.43887 (12.68°)
- C x 12: 0.44721 (12.92°)
- D x 16: 0.45951 (13.28°)
- E x 24: 0.51764 (15.00°)
- F x 12: 0.57735 (16.78°)
- total 104 struts (6 kinds)¹⁾
- strut variance 80.2%
faces: 64 (3-sided)
- A-A-C x 12 (45.74°, 45.74°, 88.51°)
- B-B-C x 12 (59.37°, 59.37°, 61.26°)
- B-D-E x 24 (52.98°, 56.71°, 70.32°)
- E-E-F x 12 (56.10°, 56.10°, 67.80°)
- F-F-F x 4 (60.00°, 60.00°, 60.00°)
- 5 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 4V Octahedron Dome (Human is 170cm/5'7")

Geodesic L3 Octahedron Dome (front view)

Geodesic L3 Octahedron Dome (bird view)

vertices/connectors: 41
- 4 x 3-way
- 13 x 4-way
- 24 x 6-way
L3 Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 32: 0.39018 (11.25°)
- B x 24: 0.42291 (12.21°)
- C x 24: 0.51764 (15.00°)
- D x 12: 0.54120 (15.70°)
- E x 12: 0.57735 (16.78°)
- total 104 struts (5 kinds)¹⁾
- strut variance 48.0%
faces: 64 (3-sided)
- A-A-D x 12 (46.09°, 46.09°, 87.81°)
- A-B-C x 24 (47.72°, 53.31°, 78.96°)
- B-B-D x 12 (50.22°, 50.22°, 79.56°)
- C-C-E x 12 (56.10°, 56.10°, 67.80°)
- E-E-E x 4 (60.00°, 60.00°, 60.00°)
- 5 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic L3 Octahedron Dome (Human is 170cm/5'7")

The nice thing is here, that the L3 provides at 3/8 and 5/8 also an almost even base line.

Geodesic L3 3/8 Octahedron Dome (front view)

Geodesic L3 3/8 Octahedron Dome (bird view)

vertices/connectors: 25
- 4 x 3-way
- 9 x 4-way
- 12 x 6-way
L3 3/8 Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 12: 0.39018 (11.25°)
- B x 16: 0.42291 (12.21°)
- C x 16: 0.51764 (15.00°)
- D x 4: 0.54120 (15.70°)
- E x 12: 0.57735 (16.78°)
- total 60 struts (5 kinds)¹⁾
- strut variance 48.0%
faces: 36 (3-sided)
- A-A-D x 4 (46.09°, 46.09°, 87.81°)
- A-B-C x 16 (47.72°, 53.31°, 78.96°)
- B-B-D x 4 (50.22°, 50.22°, 79.56°)
- C-C-E x 8 (56.10°, 56.10°, 67.80°)
- E-E-E x 4 (60.00°, 60.00°, 60.00°)
- 5 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 0.617 or 30.87% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic L3 3/8 Octahedron Dome (Human is 170cm/5'7")

Here again uneven base, for heavy construction leveling necessary.

Geodesic L3 5/8 Octahedron Dome (front view)

Geodesic L3 5/8 Octahedron Dome (bird view)

vertices/connectors: 53
- 13 x 4-way
- 4 x 5-way
- 36 x 6-way
L3 5/8 Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 36: 0.39018 (11.25°)
- B x 40: 0.42291 (12.21°)
- C x 32: 0.51764 (15.00°)
- D x 20: 0.54120 (15.70°)
- E x 16: 0.57735 (16.78°)
- total 144 struts (5 kinds)¹⁾
- strut variance 48.0%
faces: 92 (3-sided)
- A-A-D x 20 (46.09°, 46.09°, 87.81°)
- A-B-C x 32 (47.72°, 53.31°, 78.96°)
- B-B-D x 20 (50.22°, 50.22°, 79.56°)
- C-C-E x 16 (56.10°, 56.10°, 67.80°)
- E-E-E x 4 (60.00°, 60.00°, 60.00°)
- 5 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.408 or 70.41% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic L3 5/8 Octahedron Dome (Human is 170cm/5'7")

Here again uneven base, for heavy construction leveling necessary.

Geodesic 5V Octahedron Dome (front view)

Geodesic 5V Octahedron Dome (bird view)

vertices/connectors: 61
- 4 x 3-way
- 17 x 4-way
- 40 x 6-way
5V Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 16: 0.24437 (7.02°)
- B x 24: 0.31415 (9.04°)
- C x 16: 0.34134 (9.83°)
- D x 12: 0.34300 (9.88°)
- E x 24: 0.38859 (11.20°)
- F x 8: 0.39223 (11.31°)
- G x 24: 0.40033 (11.55°)
- H x 24: 0.43696 (12.62°)
- I x 12: 0.47140 (13.63°)
- total 160 struts (9 kinds)¹⁾
- strut variance 92.9%
faces: 100 (3-sided)
- A-A-D x 12 (45.43°, 45.43°, 89.13°)
- B-B-D x 12 (56.91°, 56.91°, 66.19°)
- B-C-G x 24 (49.33°, 55.51°, 75.16°)
- E-E-F x 12 (59.69°, 59.69°, 60.61°)
- E-G-H x 24 (55.09°, 57.65°, 67.26°)
- H-H-I x 12 (57.36°, 57.36°, 65.28°)
- I-I-I x 4 (60.00°, 60.00°, 60.00°)
- 7 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 5V Octahedron Dome (Human is 170cm/5'7")

Geodesic 6V Octahedron Dome (front view)

Geodesic 6V Octahedron Dome (bird view)

vertices/connectors: 85
- 4 x 3-way
- 21 x 4-way
- 60 x 6-way
6V Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 16: 0.19708 (5.66°)
- B x 24: 0.24197 (6.95°)
- C x 16: 0.26547 (7.63°)
- D x 12: 0.27735 (7.97°)
- E x 24: 0.29603 (8.51°)
- F x 40: 0.32036 (9.22°)
- G x 48: 0.33193 (9.55°)
- H x 24: 0.37796 (10.89°)
- I x 24: 0.38518 (11.10°)
- total 228 struts (9 kinds)¹⁾
- strut variance 95.4%
faces: 144 (3-sided)
- A-A-D x 12 (45.30°, 45.30°, 89.41°)
- B-B-D x 12 (55.04°, 55.04°, 69.91°)
- B-C-F x 24 (47.66°, 54.19°, 78.15°)
- E-F-G x 48 (53.94°, 61.05°, 65.02°)
- G-G-H x 24 (55.29°, 55.29°, 69.42°)
- H-I-I x 24 (58.77°, 60.62°, 60.62°)
- 6 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 6V Octahedron Dome (Human is 170cm/5'7")

Geodesic 2V.3V Octahedron Dome (front view)

Geodesic 2V.3V Octahedron Dome (bird view)

vertices/connectors: 85
- 4 x 3-way
- 21 x 4-way
- 60 x 6-way
2V.3V Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 32: 0.25480 (7.32°)
- B x 16: 0.27355 (7.86°)
- C x 24: 0.27468 (7.89°)
- D x 24: 0.27569 (7.92°)
- E x 24: 0.29082 (8.36°)
- F x 24: 0.33193 (9.55°)
- G x 12: 0.35741 (10.29°)
- H x 24: 0.36346 (10.47°)
- I x 24: 0.37796 (10.89°)
- J x 24: 0.38518 (11.10°)
- total 228 struts (10 kinds)¹⁾
- strut variance 51.2%
faces: 144 (3-sided)
- A-A-G x 12 (45.47°, 45.47°, 89.07°)
- A-D-F x 24 (48.51°, 54.14°, 77.35°)
- B-C-H x 24 (48.34°, 48.60°, 83.05°)
- C-C-G x 12 (49.42°, 49.42°, 81.16°)
- D-E-H x 24 (48.28°, 51.94°, 79.78°)
- E-E-I x 12 (49.46°, 49.46°, 81.07°)
- F-F-I x 12 (55.29°, 55.29°, 69.42°)
- I-J-J x 24 (58.77°, 60.62°, 60.62°)
- 8 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 2V.3V Octahedron Dome (Human is 170cm/5'7")

Geodesic 3V.2V Octahedron Dome (front view)

Geodesic 3V.2V Octahedron Dome (bird view)

vertices/connectors: 85
- 4 x 3-way
- 21 x 4-way
- 60 x 6-way
3V.2V Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 32: 0.23131 (6.64°)
- B x 24: 0.23773 (6.83°)
- C x 40: 0.32036 (9.22°)
- D x 12: 0.32492 (9.35°)
- E x 24: 0.33571 (9.66°)
- F x 48: 0.34069 (9.81°)
- G x 48: 0.35506 (10.23°)
- total 228 struts (7 kinds)¹⁾
- strut variance 53.5%
faces: 144 (3-sided)
- A-A-D x 12 (45.39°, 45.39°, 89.23°)
- A-B-C x 24 (46.08°, 47.75°, 86.17°)
- B-B-D x 12 (46.89°, 46.89°, 86.22°)
- C-F-G x 48 (54.79°, 60.32°, 64.89°)
- E-F-F x 24 (59.03°, 60.48°, 60.48°)
- E-G-G x 24 (56.42°, 61.79°, 61.79°)
- 6 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 3V.2V Octahedron Dome (Human is 170cm/5'7")

Geodesic 7V Octahedron Dome (front view)

Geodesic 7V Octahedron Dome (bird view)

vertices/connectors: 113
- 4 x 3-way
- 25 x 4-way
- 84 x 6-way
7V Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 16: 0.16496 (4.73°)
- B x 24: 0.19598 (5.62°)
- C x 16: 0.21494 (6.17°)
- D x 12: 0.23250 (6.68°)
- E x 24: 0.23440 (6.73°)
- F x 24: 0.26112 (7.50°)
- G x 16: 0.26224 (7.53°)
- H x 24: 0.26495 (7.61°)
- I x 24: 0.27001 (7.76°)
- J x 24: 0.28228 (8.11°)
- K x 8: 0.28284 (8.13°)
- L x 24: 0.30770 (8.85°)
- M x 12: 0.30861 (8.88°)
- N x 24: 0.31244 (8.99°)
- O x 24: 0.32892 (9.47°)
- P x 12: 0.34300 (9.88°)
- total 308 struts (16 kinds)¹⁾
- strut variance 107.9%
faces: 196 (3-sided)
- A-A-D x 12 (45.21°, 45.21°, 89.59°)
- B-B-D x 12 (53.62°, 53.62°, 72.76°)
- B-C-H x 24 (46.78°, 53.04°, 80.18°)
- E-F-H x 24 (52.91°, 62.69°, 64.40°)
- E-G-J x 24 (50.83°, 60.14°, 69.03°)
- F-F-M x 12 (53.77°, 53.77°, 72.45°)
- I-I-K x 12 (58.42°, 58.42°, 63.16°)
- I-J-N x 24 (53.71°, 57.44°, 68.85°)
- L-L-M x 12 (59.90°, 59.90°, 60.19°)
- L-N-O x 24 (57.28°, 58.66°, 64.06°)
- O-O-P x 12 (58.57°, 58.57°, 62.86°)
- P-P-P x 4 (60.00°, 60.00°, 60.00°)
- 12 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 7V Octahedron Dome (Human is 170cm/5'7")

Geodesic 8V Octahedron Dome (front view)

Geodesic 8V Octahedron Dome (bird view)

vertices/connectors: 145
- 4 x 3-way
- 29 x 4-way
- 112 x 6-way
8V Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 16: 0.14178 (4.07°)
- B x 24: 0.16439 (4.71°)
- C x 16: 0.17961 (5.15°)
- D x 24: 0.19238 (5.52°)
- E x 12: 0.20000 (5.74°)
- F x 24: 0.21272 (6.11°)
- G x 16: 0.21823 (6.26°)
- H x 24: 0.22192 (6.37°)
- I x 24: 0.22504 (6.46°)
- J x 24: 0.24197 (6.95°)
- K x 24: 0.24229 (6.96°)
- L x 16: 0.24437 (7.02°)
- M x 24: 0.24915 (7.16°)
- N x 24: 0.25786 (7.41°)
- O x 12: 0.25820 (7.42°)
- P x 24: 0.27685 (7.96°)
- Q x 12: 0.27735 (7.97°)
- R x 24: 0.28011 (8.05°)
- S x 24: 0.29180 (8.39°)
- T x 12: 0.30151 (8.67°)
- total 400 struts (20 kinds)¹⁾
- strut variance 112.6%
faces: 256 (3-sided)
- A-A-E x 12 (45.15°, 45.15°, 89.69°)
- B-B-E x 12 (52.54°, 52.54°, 74.93°)
- B-C-I x 24 (46.28°, 52.15°, 81.57°)
- D-F-I x 24 (52.06°, 60.68°, 67.26°)
- D-G-K x 24 (49.05°, 58.93°, 72.02°)
- F-F-O x 12 (52.63°, 52.63°, 74.74°)
- H-J-L x 24 (54.28°, 62.31°, 63.41°)
- H-K-N x 24 (52.56°, 60.11°, 67.34°)
- J-J-Q x 12 (55.04°, 55.04°, 69.91°)
- M-M-O x 12 (58.80°, 58.80°, 62.40°)
- M-N-R x 24 (55.00°, 57.97°, 67.03°)
- P-P-Q x 12 (59.94°, 59.94°, 60.12°)
- P-R-S x 24 (57.85°, 58.95°, 63.19°)
- S-S-T x 12 (58.89°, 58.89°, 62.21°)
- T-T-T x 4 (60.00°, 60.00°, 60.00°)
- 15 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 8V Octahedron Dome (Human is 170cm/5'7")

Geodesic L4 Octahedron Dome (front view)

Geodesic L4 Octahedron Dome (bird view)

vertices/connectors: 145
- 4 x 3-way
- 29 x 4-way
- 112 x 6-way
L4 Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 64: 0.19603 (5.62°)
- B x 24: 0.19991 (5.74°)
- C x 24: 0.20044 (5.75°)
- D x 48: 0.21266 (6.10°)
- E x 24: 0.21671 (6.22°)
- F x 24: 0.21746 (6.24°)
- G x 48: 0.26105 (7.50°)
- H x 24: 0.26433 (7.59°)
- I x 24: 0.26899 (7.73°)
- J x 24: 0.27316 (7.85°)
- K x 12: 0.27590 (7.93°)
- L x 12: 0.27686 (7.96°)
- M x 24: 0.29180 (8.39°)
- N x 12: 0.29886 (8.59°)
- O x 12: 0.30151 (8.67°)
- total 400 struts (15 kinds)¹⁾
- strut variance 53.8%
faces: 256 (3-sided)
- A-A-K x 12 (45.27°, 45.27°, 89.47°)
- A-B-J x 24 (45.78°, 46.96°, 87.27°)
- A-D-H x 24 (47.00°, 52.53°, 80.47°)
- A-E-G x 24 (47.32°, 54.37°, 78.32°)
- B-B-K x 12 (46.36°, 46.36°, 87.28°)
- C-D-G x 24 (48.74°, 52.92°, 78.34°)
- C-E-H x 24 (48.00°, 53.47°, 78.53°)
- D-D-L x 12 (49.39°, 49.39°, 81.22°)
- D-F-J x 24 (49.80°, 51.36°, 78.84°)
- F-F-L x 12 (50.46°, 50.46°, 79.07°)
- G-G-N x 12 (55.08°, 55.08°, 69.83°)
- G-I-M x 24 (55.32°, 57.91°, 66.78°)
- I-I-N x 12 (56.25°, 56.25°, 67.50°)
- M-M-O x 12 (58.89°, 58.89°, 62.21°)
- O-O-O x 4 (60.00°, 60.00°, 60.00°)
- 15 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic L4 Octahedron Dome (Human is 170cm/5'7")

Now the advantage of L3 vs 4V is more apparent, the L3 has various almost even horizontal bases where 4V has only one at 1/2 height.

So, let's explore 7/16 and 9/16 variants as well.

Geodesic L4 7/16 Octahedron Dome (front view)

Geodesic L4 7/16 Octahedron Dome (bird view)

vertices/connectors: 113
- 4 x 3-way
- 25 x 4-way
- 84 x 6-way
L4 7/16 Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 28: 0.19603 (5.62°)
- B x 16: 0.19991 (5.74°)
- C x 24: 0.20044 (5.75°)
- D x 40: 0.21266 (6.10°)
- E x 16: 0.21671 (6.22°)
- F x 24: 0.21746 (6.24°)
- G x 40: 0.26105 (7.50°)
- H x 16: 0.26433 (7.59°)
- I x 24: 0.26899 (7.73°)
- J x 16: 0.27316 (7.85°)
- K x 4: 0.27590 (7.93°)
- L x 12: 0.27686 (7.96°)
- M x 24: 0.29180 (8.39°)
- N x 12: 0.29886 (8.59°)
- O x 12: 0.30151 (8.67°)
- total 308 struts (15 kinds)¹⁾
- strut variance 53.8%
faces: 196 (3-sided)
- A-A-K x 4 (45.27°, 45.27°, 89.47°)
- A-B-J x 16 (45.78°, 46.96°, 87.27°)
- A-D-H x 16 (47.00°, 52.53°, 80.47°)
- A-E-G x 16 (47.32°, 54.37°, 78.32°)
- B-B-K x 4 (46.36°, 46.36°, 87.28°)
- C-D-G x 24 (48.74°, 52.92°, 78.34°)
- C-E-H x 16 (48.00°, 53.47°, 78.53°)
- D-D-L x 12 (49.39°, 49.39°, 81.22°)
- D-F-J x 16 (49.80°, 51.36°, 78.84°)
- F-F-L x 12 (50.46°, 50.46°, 79.07°)
- G-G-N x 8 (55.08°, 55.08°, 69.83°)
- G-I-M x 24 (55.32°, 57.91°, 66.78°)
- I-I-N x 12 (56.25°, 56.25°, 67.50°)
- M-M-O x 12 (58.89°, 58.89°, 62.21°)
- O-O-O x 4 (60.00°, 60.00°, 60.00°)
- 15 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 0.805 or 40.25% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic L4 7/16 Octahedron Dome (Human is 170cm/5'7")

Geodesic L4 9/16 Octahedron Dome (front view)

Geodesic L4 9/16 Octahedron Dome (bird view)

vertices/connectors: 173
- 29 x 4-way
- 4 x 5-way
- 140 x 6-way
L4 9/16 Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 68: 0.19603 (5.62°)
- B x 40: 0.19991 (5.74°)
- C x 32: 0.20044 (5.75°)
- D x 56: 0.21266 (6.10°)
- E x 32: 0.21671 (6.22°)
- F x 32: 0.21746 (6.24°)
- G x 56: 0.26105 (7.50°)
- H x 32: 0.26433 (7.59°)
- I x 24: 0.26899 (7.73°)
- J x 32: 0.27316 (7.85°)
- K x 20: 0.27590 (7.93°)
- L x 12: 0.27686 (7.96°)
- M x 24: 0.29180 (8.39°)
- N x 16: 0.29886 (8.59°)
- O x 12: 0.30151 (8.67°)
- total 488 struts (15 kinds)¹⁾
- strut variance 53.8%
faces: 316 (3-sided)
- A-A-K x 20 (45.27°, 45.27°, 89.47°)
- A-B-J x 32 (45.78°, 46.96°, 87.27°)
- A-D-H x 32 (47.00°, 52.53°, 80.47°)
- A-E-G x 32 (47.32°, 54.37°, 78.32°)
- B-B-K x 20 (46.36°, 46.36°, 87.28°)
- C-D-G x 24 (48.74°, 52.92°, 78.34°)
- C-E-H x 32 (48.00°, 53.47°, 78.53°)
- D-D-L x 12 (49.39°, 49.39°, 81.22°)
- D-F-J x 32 (49.80°, 51.36°, 78.84°)
- F-F-L x 12 (50.46°, 50.46°, 79.07°)
- G-G-N x 16 (55.08°, 55.08°, 69.83°)
- G-I-M x 24 (55.32°, 57.91°, 66.78°)
- I-I-N x 12 (56.25°, 56.25°, 67.50°)
- M-M-O x 12 (58.89°, 58.89°, 62.21°)
- O-O-O x 4 (60.00°, 60.00°, 60.00°)
- 15 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.211 or 60.57% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic L4 9/16 Octahedron Dome (Human is 170cm/5'7")

The L4 6/16 and 10/16 Octahedron Dome would be also possible, but the leveling gets already bigger as you see.

L4 6/16 Octahedron Dome

L4 10/16 Octahedron Dome

Geodesic 9V Octahedron Dome (front view)

Geodesic 9V Octahedron Dome (bird view)

vertices/connectors: 181
- 4 x 3-way
- 33 x 4-way
- 144 x 6-way
9V Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 16: 0.12427 (3.56°)
- B x 24: 0.14146 (4.06°)
- C x 16: 0.15379 (4.41°)
- D x 24: 0.16250 (4.66°)
- E x 12: 0.17541 (5.03°)
- F x 24: 0.17837 (5.12°)
- G x 16: 0.18508 (5.31°)
- H x 24: 0.18597 (5.34°)
- I x 24: 0.19519 (5.60°)
- J x 48: 0.20635 (5.92°)
- K x 40: 0.21070 (6.05°)
- L x 48: 0.21572 (6.19°)
- M x 20: 0.22086 (6.34°)
- N x 24: 0.23223 (6.67°)
- O x 48: 0.24080 (6.92°)
- P x 48: 0.24592 (7.06°)
- Q x 24: 0.26261 (7.55°)
- R x 24: 0.26495 (7.61°)
- total 504 struts (18 kinds)¹⁾
- strut variance 113.2%
faces: 324 (3-sided)
- A-A-E x 12 (45.13°, 45.13°, 89.75°)
- B-B-E x 12 (51.70°, 51.70°, 76.60°)
- B-C-I x 24 (45.97°, 51.39°, 82.64°)
- D-F-I x 24 (51.32°, 58.99°, 69.68°)
- D-G-K x 24 (47.94°, 57.75°, 74.30°)
- F-F-M x 12 (51.75°, 51.75°, 76.50°)
- H-K-L x 48 (51.71°, 62.76°, 65.53°)
- J-J-M x 24 (57.65°, 57.65°, 64.70°)
- J-L-O x 48 (53.42°, 57.05°, 69.53°)
- N-O-P x 48 (56.98°, 60.40°, 62.62°)
- P-P-Q x 24 (57.73°, 57.73°, 64.55°)
- Q-R-R x 24 (59.40°, 60.30°, 60.30°)
- 12 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 9V Octahedron Dome (Human is 170cm/5'7")

Geodesic 3V.3V Octahedron Dome (front view)

Geodesic 3V.3V Octahedron Dome (bird view)

vertices/connectors: 181
- 4 x 3-way
- 33 x 4-way
- 144 x 6-way
3V.3V Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 32: 0.15315 (4.39°)
- B x 16: 0.15689 (4.50°)
- C x 24: 0.15697 (4.50°)
- D x 24: 0.15706 (4.50°)
- E x 24: 0.16057 (4.60°)
- F x 40: 0.21070 (6.05°)
- G x 12: 0.21595 (6.20°)
- H x 24: 0.21723 (6.24°)
- I x 20: 0.22086 (6.34°)
- J x 24: 0.22224 (6.38°)
- K x 96: 0.22365 (6.42°)
- L x 48: 0.23512 (6.75°)
- M x 24: 0.23594 (6.77°)
- N x 48: 0.23610 (6.78°)
- O x 48: 0.23760 (6.82°)
- total 504 struts (15 kinds)¹⁾
- strut variance 55.1%
faces: 324 (3-sided)
- A-A-G x 12 (45.17°, 45.17°, 89.65°)
- A-D-F x 24 (46.46°, 48.02°, 85.52°)
- B-C-H x 24 (46.20°, 46.24°, 87.57°)
- C-C-G x 12 (46.54°, 46.54°, 86.93°)
- D-E-H x 24 (46.20°, 47.55°, 86.25°)
- E-E-I x 12 (46.55°, 46.55°, 86.90°)
- F-K-L x 48 (54.62°, 59.91°, 65.47°)
- I-N-N x 24 (55.78°, 62.11°, 62.11°)
- J-K-K x 24 (59.59°, 60.21°, 60.21°)
- J-O-O x 24 (55.76°, 62.12°, 62.12°)
- K-L-N x 48 (56.66°, 61.45°, 61.90°)
- K-M-O x 48 (56.36°, 61.44°, 62.21°)
- 12 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 3V.3V Octahedron Dome (Human is 170cm/5'7")

Geodesic 10V Octahedron Dome (front view)

Geodesic 10V Octahedron Dome (bird view)

vertices/connectors: 221
- 4 x 3-way
- 37 x 4-way
- 180 x 6-way
10V Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 16: 0.11060 (3.17°)
- B x 24: 0.12408 (3.56°)
- C x 16: 0.13422 (3.85°)
- D x 24: 0.14037 (4.02°)
- E x 24: 0.15305 (4.39°)
- F x 12: 0.15617 (4.48°)
- G x 24: 0.15897 (4.56°)
- H x 16: 0.15974 (4.58°)
- I x 24: 0.17214 (4.94°)
- J x 24: 0.17475 (5.01°)
- K x 24: 0.17715 (5.08°)
- L x 16: 0.18286 (5.25°)
- M x 24: 0.18357 (5.27°)
- N x 24: 0.18563 (5.33°)
- O x 24: 0.18984 (5.45°)
- P x 12: 0.19245 (5.52°)
- Q x 24: 0.19270 (5.53°)
- R x 24: 0.19673 (5.65°)
- S x 16: 0.19708 (5.66°)
- T x 24: 0.20840 (5.98°)
- U x 24: 0.20865 (5.99°)
- V x 24: 0.20967 (6.02°)
- W x 24: 0.21329 (6.12°)
- X x 24: 0.21808 (6.26°)
- Y x 12: 0.21822 (6.26°)
- Z x 24: 0.22923 (6.58°)
- AA x 12: 0.22942 (6.59°)
- AB x 24: 0.23096 (6.63°)
- AC x 24: 0.23738 (6.82°)
- AD x 12: 0.24254 (6.97°)
- total 620 struts (30 kinds)¹⁾
- strut variance 119.3%
faces: 400 (3-sided)
- A-A-F x 12 (45.08°, 45.08°, 89.84°)
- AA-U-U x 12 (66.68°, 56.66°, 56.66°)
- AA-Z-Z x 12 (60.06°, 59.97°, 59.97°)
- AB-AC-Z x 24 (59.32°, 62.11°, 58.57°)
- AB-W-X x 24 (64.74°, 56.62°, 58.64°)
- AC-AC-AD x 12 (59.29°, 59.29°, 61.43°)
- AD-AD-AD x 4 (60.00°, 60.00°, 60.00°)
- B-B-F x 12 (51.00°, 51.00°, 78.00°)
- B-C-I x 24 (45.76°, 50.78°, 83.46°)
- D-E-I x 24 (50.76°, 57.56°, 71.68°)
- D-H-N x 24 (47.25°, 56.64°, 76.11°)
- E-E-P x 12 (51.02°, 51.02°, 77.97°)
- G-L-Q x 24 (50.01°, 61.80°, 68.20°)
- G-M-N x 24 (51.02°, 63.84°, 65.14°)
- J-J-P x 12 (56.57°, 56.57°, 66.86°)
- J-M-V x 24 (52.23°, 56.18°, 71.59°)
- K-O-S x 24 (54.48°, 60.66°, 64.86°)
- K-Q-T x 24 (52.26°, 59.31°, 68.43°)
- O-O-Y x 12 (54.91°, 54.91°, 70.17°)
- R-T-X x 24 (54.87°, 60.06°, 65.07°)
- R-U-V x 24 (56.08°, 61.70°, 62.22°)
- W-W-Y x 12 (59.24°, 59.24°, 61.53°)
- 22 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 10V Octahedron Dome (Human is 170cm/5'7")

Geodesic 2V.5V Octahedron Dome (front view)

Geodesic 2V.5V Octahedron Dome (bird view)

vertices/connectors: 221
- 4 x 3-way
- 37 x 4-way
- 180 x 6-way
2V.5V Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 32: 0.14897 (4.27°)
- B x 24: 0.15701 (4.50°)
- C x 24: 0.15942 (4.57°)
- D x 32: 0.16077 (4.61°)
- E x 24: 0.16200 (4.65°)
- F x 24: 0.16287 (4.67°)
- G x 16: 0.16512 (4.74°)
- H x 24: 0.16655 (4.78°)
- I x 24: 0.16939 (4.86°)
- J x 24: 0.17295 (4.96°)
- K x 24: 0.17327 (4.97°)
- L x 24: 0.17393 (4.99°)
- M x 24: 0.17615 (5.05°)
- N x 24: 0.18984 (5.45°)
- O x 24: 0.20577 (5.91°)
- P x 12: 0.21009 (6.03°)
- Q x 24: 0.21329 (6.12°)
- R x 24: 0.21561 (6.19°)
- S x 24: 0.21702 (6.23°)
- T x 24: 0.21808 (6.26°)
- U x 12: 0.21822 (6.26°)
- V x 12: 0.22654 (6.50°)
- W x 24: 0.22702 (6.52°)
- X x 24: 0.22923 (6.58°)
- Y x 12: 0.22942 (6.59°)
- Z x 24: 0.23096 (6.63°)
- AA x 24: 0.23738 (6.82°)
- AB x 12: 0.24254 (6.97°)
- total 620 struts (28 kinds)¹⁾
- strut variance 62.8%
faces: 400 (3-sided)
- A-A-P x 12 (45.17°, 45.17°, 89.66°)
- A-C-N x 24 (49.58°, 54.54°, 75.88°)
- AA-AA-AB x 12 (59.29°, 59.29°, 61.43°)
- AA-X-Z x 24 (62.11°, 58.57°, 59.32°)
- AB-AB-AB x 4 (60.00°, 60.00°, 60.00°)
- B-B-P x 12 (48.00°, 48.00°, 84.00°)
- B-D-S x 24 (46.21°, 47.67°, 86.12°)
- C-H-O x 24 (49.32°, 52.43°, 78.26°)
- D-F-O x 24 (50.07°, 50.98°, 78.95°)
- E-G-R x 24 (48.15°, 49.39°, 82.46°)
- E-I-S x 24 (47.63°, 50.59°, 81.78°)
- F-J-R x 24 (48.05°, 52.12°, 79.83°)
- H-K-T x 24 (48.75°, 51.45°, 79.80°)
- I-I-V x 12 (48.05°, 48.05°, 83.91°)
- J-L-W x 24 (48.92°, 49.31°, 81.77°)
- K-M-W x 24 (48.94°, 50.06°, 81.00°)
- L-L-V x 12 (49.37°, 49.37°, 81.27°)
- M-M-Y x 12 (49.39°, 49.39°, 81.23°)
- N-N-U x 12 (54.91°, 54.91°, 70.17°)
- Q-Q-U x 12 (59.24°, 59.24°, 61.53°)
- Q-T-Z x 24 (56.62°, 58.64°, 64.74°)
- X-X-Y x 12 (59.97°, 59.97°, 60.06°)
- 22 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 2V.5V Octahedron Dome (Human is 170cm/5'7")

Geodesic 5V.2V Octahedron Dome (front view)

Geodesic 5V.2V Octahedron Dome (bird view)

vertices/connectors: 221
- 4 x 3-way
- 37 x 4-way
- 180 x 6-way
5V.2V Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 32: 0.12241 (3.51°)
- B x 24: 0.12334 (3.54°)
- C x 48: 0.15757 (4.52°)
- D x 24: 0.15923 (4.57°)
- E x 24: 0.15977 (4.58°)
- F x 32: 0.17130 (4.91°)
- G x 24: 0.17214 (4.94°)
- H x 12: 0.17279 (4.96°)
- I x 24: 0.17332 (4.97°)
- J x 12: 0.17365 (4.98°)
- K x 48: 0.19523 (5.60°)
- L x 16: 0.19708 (5.66°)
- M x 24: 0.19810 (5.68°)
- N x 24: 0.19866 (5.70°)
- O x 12: 0.19993 (5.74°)
- P x 48: 0.20119 (5.77°)
- Q x 24: 0.20290 (5.82°)
- R x 24: 0.20452 (5.87°)
- S x 48: 0.21981 (6.31°)
- T x 24: 0.22285 (6.40°)
- U x 24: 0.22431 (6.44°)
- V x 24: 0.23738 (6.82°)
- W x 12: 0.24154 (6.94°)
- X x 12: 0.24254 (6.97°)
- total 620 struts (24 kinds)¹⁾
- strut variance 98.1%
faces: 400 (3-sided)
- A-A-H x 12 (45.10°, 45.10°, 89.80°)
- A-B-G x 24 (45.32°, 45.75°, 88.93°)
- B-B-H x 12 (45.51°, 45.51°, 88.97°)
- C-C-J x 12 (56.58°, 56.58°, 66.84°)
- C-D-G x 24 (56.65°, 57.54°, 65.81°)
- C-F-Q x 24 (48.92°, 55.02°, 76.05°)
- C-I-P x 24 (49.08°, 56.19°, 74.73°)
- D-D-J x 12 (56.96°, 56.96°, 66.08°)
- E-F-P x 24 (50.02°, 55.23°, 74.75°)
- E-I-Q x 24 (49.51°, 55.56°, 74.93°)
- K-K-O x 12 (59.20°, 59.20°, 61.60°)
- K-L-M x 24 (59.20°, 60.15°, 60.66°)
- K-P-T x 24 (54.53°, 57.09°, 68.38°)
- K-R-S x 24 (54.64°, 58.69°, 66.67°)
- M-M-O x 12 (59.70°, 59.70°, 60.60°)
- N-P-S x 24 (56.12°, 57.20°, 66.68°)
- N-R-T x 24 (55.22°, 57.71°, 67.07°)
- S-S-W x 12 (56.68°, 56.68°, 66.65°)
- S-U-V x 24 (56.77°, 58.61°, 64.62°)
- U-U-W x 12 (57.43°, 57.43°, 65.14°)
- V-V-X x 12 (59.29°, 59.29°, 61.43°)
- X-X-X x 4 (60.00°, 60.00°, 60.00°)
- 22 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 5V.2V Octahedron Dome (Human is 170cm/5'7")

Cube

Uniform Polyhedron: U6
aka Hexahedron
Platonic Solid
Platonic Element: Earth
Vertices: 8
Edges: 12
Faces: 6
Wythoff symbol: 3|2 4
Symmetry Group: octahedral
Vertex Configuration: {4, 4, 4}
Dual: octahedron
V: s³
A: s² * 6
r_inner: s / 2
r_outer: s / 2 * √3

Cube L0/0V (original)

Cube L1/1V flat (only triangles & flat)

Cube L1/1V (only triangles & normalized)

The 6 squares are triangulated for further processing.

Geodesic 1V Cube Dome (front view)

Geodesic 1V Cube Dome (bird view)

vertices/connectors: 10
- 2 x 3-way
- 6 x 4-way
- 2 x 6-way
1V Cube Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 14: 0.91940 (27.37°)
- B x 7: 1.15470 (35.26°)
- total 21 struts (2 kinds)¹⁾
- strut variance 25.6%
faces: 12 (3-sided)
- A-A-B x 12 (51.10°, 51.10°, 77.80°)
diameter: 2.000, radius: 1.000
height: 0.817 or 40.83% of diameter

Geodesic 1V Cube Dome (Human is 170cm/5'7")

Geodesic 2V Cube Dome (front view)

Geodesic 2V Cube Dome (bird view)

vertices/connectors: 31
- 2 x 3-way
- 12 x 4-way
- 17 x 6-way
2V Cube Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 28: 0.47313 (13.68°)
- B x 24: 0.53327 (15.46°)
- C x 14: 0.60581 (17.63°)
- D x 12: 0.65012 (18.97°)
- total 78 struts (4 kinds)¹⁾
- strut variance 37.4%
faces: 48 (3-sided)
- A-A-D x 12 (46.60°, 46.60°, 86.80°)
- A-B-C x 24 (48.57°, 57.69°, 73.75°)
- B-B-D x 12 (52.45°, 52.45°, 75.11°)
- 3 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 2V Cube Dome (Human is 170cm/5'7")

Geodesic 3V Cube Dome (front view)

Geodesic 3V Cube Dome (bird view)

vertices/connectors: 64
- 2 x 3-way
- 18 x 4-way
- 44 x 6-way
3V Cube Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 28: 0.30559 (8.79°)
- B x 14: 0.34007 (9.79°)
- C x 6: 0.34314 (9.88°)
- D x 18: 0.34315 (9.88°)
- E x 24: 0.34511 (9.94°)
- F x 24: 0.36954 (10.65°)
- G x 14: 0.38165 (11.00°)
- H x 12: 0.42710 (12.33°)
- I x 24: 0.43771 (12.64°)
- J x 7: 0.45883 (13.26°)
- total 171 struts (10 kinds)¹⁾
- strut variance 50.1%
faces: 108 (3-sided)
- A-A-H x 12 (45.67°, 45.67°, 88.66°)
- A-E-G x 24 (49.42°, 59.06°, 71.52°)
- B-C-I x 6 (49.86°, 50.46°, 79.68°)
- B-D-I x 18 (49.85°, 50.48°, 79.67°)
- C-D-H x 6 (51.50°, 51.52°, 76.97°)
- D-D-H x 6 (51.52°, 51.52°, 76.96°)
- E-F-I x 24 (49.74°, 54.80°, 75.46°)
- F-F-J x 12 (51.62°, 51.62°, 76.75°)
- 8 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 0.973 or 48.67% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 3V Cube Dome (Human is 170cm/5'7")

Geodesic 4V Cube Dome (front view)

Geodesic 4V Cube Dome (bird view)

vertices/connectors: 109
- 2 x 3-way
- 24 x 4-way
- 83 x 6-way
4V Cube Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 28: 0.22393 (6.43°)
- B x 24: 0.24654 (7.08°)
- C x 24: 0.25137 (7.22°)
- D x 28: 0.25259 (7.26°)
- E x 24: 0.25756 (7.40°)
- F x 24: 0.26734 (7.68°)
- G x 14: 0.27477 (7.90°)
- H x 24: 0.27584 (7.93°)
- I x 24: 0.28059 (8.06°)
- J x 24: 0.31367 (9.02°)
- K x 12: 0.31469 (9.05°)
- L x 24: 0.32956 (9.48°)
- M x 14: 0.33820 (9.74°)
- N x 12: 0.35141 (10.12°)
- total 300 struts (14 kinds)¹⁾
- strut variance 56.9%
faces: 192 (3-sided)
- A-A-K x 12 (45.35°, 45.35°, 89.30°)
- A-C-G x 24 (50.12°, 59.51°, 70.37°)
- B-B-K x 12 (50.33°, 50.33°, 79.34°)
- B-D-L x 24 (47.88°, 49.47°, 82.65°)
- C-F-J x 24 (50.51°, 55.14°, 74.36°)
- D-E-J x 24 (51.34°, 52.78°, 75.88°)
- E-H-L x 24 (49.39°, 54.37°, 76.24°)
- F-I-M x 24 (50.13°, 53.68°, 76.19°)
- H-H-N x 12 (50.43°, 50.43°, 79.15°)
- I-I-N x 12 (51.23°, 51.23°, 77.53°)
- 10 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 4V Cube Dome (Human is 170cm/5'7")

Geodesic L3 Cube Dome (front view)

Geodesic L3 Cube Dome (bird view)

vertices/connectors: 109
- 2 x 3-way
- 24 x 4-way
- 83 x 6-way
L3 Cube Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 56: 0.23826 (6.84°)
- B x 24: 0.24530 (7.05°)
- C x 24: 0.24658 (7.08°)
- D x 48: 0.26908 (7.73°)
- E x 24: 0.27641 (7.94°)
- F x 24: 0.27864 (8.01°)
- G x 28: 0.30653 (8.82°)
- H x 24: 0.31291 (9.00°)
- I x 24: 0.32956 (9.48°)
- J x 12: 0.33455 (9.63°)
- K x 12: 0.33727 (9.71°)
- total 300 struts (11 kinds)¹⁾
- strut variance 41.5%
faces: 192 (3-sided)
- A-A-J x 12 (45.41°, 45.41°, 89.18°)
- A-B-I x 24 (46.15°, 47.93°, 85.92°)
- A-D-H x 24 (47.61°, 56.51°, 75.88°)
- A-E-G x 24 (47.92°, 59.41°, 72.67°)
- B-B-J x 12 (47.00°, 47.00°, 86.00°)
- C-D-G x 24 (50.22°, 57.00°, 72.78°)
- C-E-H x 24 (48.99°, 57.76°, 73.24°)
- D-D-K x 12 (51.19°, 51.19°, 77.62°)
- D-F-I x 24 (51.69°, 54.33°, 73.97°)
- F-F-K x 12 (52.75°, 52.75°, 74.51°)
- 10 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic L3 Cube Dome (Human is 170cm/5'7")

Geodesic 5V Cube Dome (front view)

Geodesic 5V Cube Dome (bird view)

vertices/connectors: 166
- 2 x 3-way
- 30 x 4-way
- 134 x 6-way
5V Cube Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 28: 0.17629 (5.06°)
- B x 24: 0.19100 (5.48°)
- C x 24: 0.19686 (5.65°)
- D x 28: 0.19765 (5.67°)
- E x 24: 0.20103 (5.77°)
- F x 24: 0.20327 (5.83°)
- G x 38: 0.20588 (5.91°)
- H x 14: 0.21382 (6.14°)
- I x 24: 0.21400 (6.14°)
- J x 24: 0.21992 (6.31°)
- K x 24: 0.22028 (6.32°)
- L x 24: 0.22264 (6.39°)
- M x 24: 0.22437 (6.44°)
- N x 24: 0.24051 (6.91°)
- O x 12: 0.24834 (7.13°)
- P x 24: 0.25832 (7.42°)
- Q x 14: 0.26002 (7.47°)
- R x 24: 0.26089 (7.50°)
- S x 24: 0.27779 (7.98°)
- T x 12: 0.27793 (7.99°)
- U x 7: 0.28006 (8.05°)
- total 465 struts (21 kinds)¹⁾
- strut variance 58.9%
faces: 300 (3-sided)
- A-A-O x 12 (45.24°, 45.24°, 89.53°)
- A-C-H x 24 (50.64°, 59.71°, 69.65°)
- B-B-O x 12 (49.46°, 49.46°, 81.08°)
- B-D-R x 24 (46.76°, 48.91°, 84.33°)
- C-G-N x 24 (51.64°, 55.08°, 73.28°)
- D-F-N x 24 (52.06°, 54.23°, 73.71°)
- E-G-P x 24 (49.76°, 51.44°, 78.80°)
- E-I-R x 24 (48.86°, 53.30°, 77.84°)
- F-J-P x 24 (49.52°, 55.36°, 75.12°)
- G-K-Q x 24 (49.93°, 54.97°, 75.10°)
- I-I-T x 12 (49.51°, 49.51°, 80.98°)
- J-L-S x 24 (50.68°, 51.55°, 77.77°)
- K-M-S x 24 (50.68°, 52.00°, 77.31°)
- L-L-T x 12 (51.38°, 51.38°, 77.25°)
- M-M-U x 12 (51.38°, 51.38°, 77.23°)
- 15 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 0.990 or 49.51% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 5V Cube Dome (Human is 170cm/5'7")

Geodesic 6V Cube Dome (front view)

Geodesic 6V Cube Dome (bird view)

vertices/connectors: 235
- 2 x 3-way
- 36 x 4-way
- 197 x 6-way
6V Cube Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 28: 0.14523 (4.16°)
- B x 24: 0.15547 (4.46°)
- C x 28: 0.16126 (4.62°)
- D x 24: 0.16153 (4.63°)
- E x 24: 0.16348 (4.69°)
- F x 24: 0.16630 (4.77°)
- G x 24: 0.16695 (4.79°)
- H x 24: 0.16766 (4.81°)
- I x 28: 0.17066 (4.90°)
- J x 24: 0.17291 (4.96°)
- K x 14: 0.17475 (5.01°)
- L x 48: 0.17945 (5.15°)
- M x 24: 0.18094 (5.19°)
- N x 24: 0.18189 (5.22°)
- O x 24: 0.18285 (5.25°)
- P x 24: 0.18335 (5.26°)
- Q x 24: 0.18806 (5.40°)
- R x 24: 0.18829 (5.40°)
- S x 24: 0.19379 (5.56°)
- T x 12: 0.20485 (5.88°)
- U x 14: 0.20865 (5.99°)
- V x 24: 0.20898 (6.00°)
- W x 24: 0.21479 (6.17°)
- X x 24: 0.21657 (6.22°)
- Y x 24: 0.22440 (6.44°)
- Z x 12: 0.22766 (6.54°)
- AA x 14: 0.23096 (6.63°)
- AB x 24: 0.23140 (6.64°)
- AC x 12: 0.23682 (6.80°)
- total 666 struts (29 kinds)¹⁾
- strut variance 63.1%
faces: 432 (3-sided)
- A-A-T x 12 (45.12°, 45.12°, 89.75°)
- A-D-K x 24 (50.99°, 59.80°, 69.21°)
- AA-O-Q x 24 (77.00°, 50.49°, 52.51°)
- AB-M-N x 24 (79.26°, 50.18°, 50.56°)
- AB-P-R x 24 (76.99°, 50.55°, 52.45°)
- AC-Q-Q x 12 (78.02°, 50.99°, 50.99°)
- AC-R-R x 12 (77.92°, 51.04°, 51.04°)
- B-B-T x 12 (48.79°, 48.79°, 82.42°)
- B-C-W x 24 (46.18°, 48.46°, 85.36°)
- C-G-S x 24 (52.48°, 55.16°, 72.36°)
- D-F-S x 24 (52.62°, 54.91°, 72.47°)
- E-I-X x 24 (48.17°, 51.07°, 80.77°)
- E-J-W x 24 (48.41°, 52.28°, 79.31°)
- F-L-U x 24 (50.05°, 55.79°, 74.16°)
- G-L-V x 24 (50.19°, 55.66°, 74.15°)
- H-I-V x 24 (51.21°, 52.51°, 76.28°)
- H-N-X x 24 (48.82°, 54.73°, 76.45°)
- J-J-Z x 12 (48.82°, 48.82°, 82.37°)
- L-O-Y x 24 (51.03°, 52.43°, 76.53°)
- L-P-Y x 24 (50.99°, 52.60°, 76.41°)
- M-M-Z x 12 (51.00°, 51.00°, 78.00°)
- 21 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 6V Cube Dome (Human is 170cm/5'7")

Geodesic 2V.3V Cube Dome (front view)

Geodesic 2V.3V Cube Dome (bird view)

vertices/connectors: 235
- 2 x 3-way
- 36 x 4-way
- 197 x 6-way
2V.3V Cube Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 56: 0.15768 (4.52°)
- B x 28: 0.16179 (4.64°)
- C x 24: 0.16188 (4.64°)
- D x 24: 0.16198 (4.65°)
- E x 24: 0.16341 (4.69°)
- F x 24: 0.16345 (4.69°)
- G x 24: 0.16505 (4.73°)
- H x 24: 0.16580 (4.76°)
- I x 48: 0.17771 (5.10°)
- J x 24: 0.18291 (5.25°)
- K x 24: 0.18312 (5.25°)
- L x 24: 0.18365 (5.27°)
- M x 24: 0.18424 (5.29°)
- N x 24: 0.18444 (5.29°)
- O x 24: 0.18608 (5.34°)
- P x 24: 0.18737 (5.38°)
- Q x 28: 0.20184 (5.79°)
- R x 24: 0.20777 (5.96°)
- S x 24: 0.20826 (5.98°)
- T x 24: 0.20976 (6.02°)
- U x 14: 0.21071 (6.05°)
- V x 24: 0.21657 (6.22°)
- W x 12: 0.22230 (6.38°)
- X x 24: 0.22371 (6.42°)
- Y x 12: 0.22389 (6.43°)
- Z x 24: 0.22533 (6.47°)
- AA x 12: 0.22766 (6.54°)
- total 666 struts (27 kinds)¹⁾
- strut variance 44.4%
faces: 432 (3-sided)
- A-A-W x 12 (45.19°, 45.19°, 89.63°)
- A-D-V x 24 (46.52°, 48.19°, 85.29°)
- A-I-R x 24 (47.51°, 56.19°, 76.31°)
- A-K-Q x 24 (48.07°, 59.75°, 72.18°)
- AA-H-H x 12 (86.73°, 46.63°, 46.63°)
- AA-P-P x 12 (74.82°, 52.59°, 52.59°)
- B-C-X x 24 (46.27°, 46.30°, 87.43°)
- B-J-S x 24 (48.33°, 57.60°, 74.07°)
- C-C-W x 12 (46.64°, 46.64°, 86.71°)
- D-H-X x 24 (46.26°, 47.68°, 86.06°)
- E-J-R x 24 (48.94°, 57.56°, 73.51°)
- E-L-T x 24 (48.51°, 57.37°, 74.12°)
- F-I-Q x 24 (50.55°, 57.06°, 72.38°)
- F-O-T x 24 (48.33°, 58.24°, 73.44°)
- G-K-S x 24 (49.38°, 57.34°, 73.28°)
- G-O-U x 24 (48.69°, 57.85°, 73.46°)
- I-I-Y x 12 (50.95°, 50.95°, 78.10°)
- I-N-V x 24 (51.85°, 54.69°, 73.45°)
- L-M-Z x 24 (52.14°, 52.34°, 75.53°)
- M-M-Y x 12 (52.57°, 52.57°, 74.86°)
- N-P-Z x 24 (52.10°, 53.31°, 74.59°)
- 21 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 2V.3V Cube Dome (Human is 170cm/5'7")

Geodesic 3V.2V Cube Dome (front view)

Geodesic 3V.2V Cube Dome (bird view)

vertices/connectors: 235
- 2 x 3-way
- 36 x 4-way
- 197 x 6-way
3V.2V Cube Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 56: 0.15325 (4.39°)
- B x 24: 0.15508 (4.45°)
- C x 24: 0.15535 (4.45°)
- D x 28: 0.17066 (4.90°)
- E x 48: 0.17221 (4.94°)
- F x 72: 0.17320 (4.97°)
- G x 48: 0.17469 (5.01°)
- H x 24: 0.17506 (5.02°)
- I x 24: 0.17606 (5.05°)
- J x 48: 0.18557 (5.32°)
- K x 24: 0.18823 (5.40°)
- L x 24: 0.18867 (5.41°)
- M x 28: 0.19171 (5.50°)
- N x 24: 0.19338 (5.55°)
- O x 24: 0.21479 (6.17°)
- P x 12: 0.21609 (6.20°)
- Q x 12: 0.21676 (6.22°)
- R x 48: 0.22019 (6.32°)
- S x 24: 0.22212 (6.38°)
- T x 24: 0.22243 (6.39°)
- U x 14: 0.23096 (6.63°)
- V x 12: 0.23343 (6.70°)
- total 666 struts (22 kinds)¹⁾
- strut variance 52.3%
faces: 432 (3-sided)
- A-A-P x 12 (45.15°, 45.15°, 89.71°)
- A-B-O x 24 (45.47°, 46.20°, 88.33°)
- A-F-N x 24 (49.02°, 58.60°, 72.38°)
- A-H-M x 24 (49.12°, 59.79°, 71.10°)
- B-B-P x 12 (45.84°, 45.84°, 88.32°)
- C-F-M x 24 (50.06°, 58.77°, 71.17°)
- C-H-N x 24 (49.55°, 59.09°, 71.37°)
- D-E-S x 24 (49.34°, 49.93°, 80.74°)
- D-G-R x 24 (49.60°, 51.20°, 79.21°)
- E-E-Q x 12 (50.99°, 50.99°, 78.03°)
- E-F-R x 24 (50.19°, 50.59°, 79.21°)
- E-G-O x 24 (51.22°, 52.27°, 76.51°)
- F-G-S x 24 (50.03°, 50.63°, 79.34°)
- F-J-T x 24 (49.23°, 54.25°, 76.52°)
- F-K-R x 24 (49.43°, 55.62°, 74.95°)
- G-G-Q x 12 (51.65°, 51.65°, 76.70°)
- I-J-R x 24 (50.56°, 54.49°, 74.95°)
- I-K-T x 24 (49.95°, 54.89°, 75.17°)
- J-J-V x 12 (51.04°, 51.04°, 77.92°)
- J-L-U x 24 (51.29°, 52.50°, 76.21°)
- L-L-V x 12 (51.80°, 51.80°, 76.40°)
- 21 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 3V.2V Cube Dome (Human is 170cm/5'7")

Geodesic 7V Cube Dome (front view)

Geodesic 7V Cube Dome (bird view)

vertices/connectors: 316
- 2 x 3-way
- 42 x 4-way
- 272 x 6-way
7V Cube Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 28: 0.12343 (3.54°)
- B x 24: 0.13093 (3.75°)
- C x 28: 0.13574 (3.89°)
- D x 24: 0.13685 (3.92°)
- E x 24: 0.13724 (3.93°)
- F x 24: 0.13907 (3.99°)
- G x 24: 0.14129 (4.05°)
- H x 24: 0.14148 (4.06°)
- I x 24: 0.14293 (4.10°)
- J x 24: 0.14432 (4.14°)
- K x 28: 0.14437 (4.14°)
- L x 14: 0.14749 (4.23°)
- M x 14: 0.14764 (4.23°)
- N x 24: 0.15012 (4.30°)
- O x 24: 0.15069 (4.32°)
- P x 24: 0.15101 (4.33°)
- Q x 24: 0.15272 (4.38°)
- R x 24: 0.15313 (4.39°)
- S x 24: 0.15455 (4.43°)
- T x 24: 0.15467 (4.44°)
- U x 24: 0.15525 (4.45°)
- V x 24: 0.15929 (4.57°)
- W x 24: 0.15968 (4.58°)
- X x 24: 0.15992 (4.59°)
- Y x 24: 0.16053 (4.60°)
- Z x 24: 0.16165 (4.64°)
- AA x 24: 0.16180 (4.64°)
- AB x 14: 0.17323 (4.97°)
- AC x 24: 0.17410 (4.99°)
- AD x 12: 0.17422 (5.00°)
- AE x 24: 0.18209 (5.22°)
- AF x 24: 0.18242 (5.23°)
- AG x 24: 0.18518 (5.31°)
- AH x 24: 0.18614 (5.34°)
- AI x 8: 0.19194 (5.51°)
- AJ x 4: 0.19195 (5.51°)
- AK x 14: 0.19327 (5.55°)
- AL x 24: 0.19451 (5.58°)
- AM x 24: 0.19653 (5.64°)
- AN x 7: 0.20101 (5.77°)
- AO x 24: 0.20124 (5.77°)
- AP x 12: 0.20240 (5.81°)
- total 903 struts (42 kinds)¹⁾
- strut variance 64.0%
faces: 588 (3-sided)
- A-A-AD x 12 (45.10°, 45.10°, 89.79°)
- A-D-M x 24 (51.26°, 59.85°, 68.90°)
- AA-C-G x 24 (71.45°, 52.67°, 55.89°)
- AA-D-F x 24 (71.80°, 53.44°, 54.76°)
- AB-F-O x 24 (73.28°, 50.28°, 56.44°)
- AC-G-N x 24 (73.31°, 51.02°, 55.67°)
- AC-I-K x 24 (74.60°, 52.31°, 53.09°)
- AD-B-B x 12 (83.43°, 48.29°, 48.29°)
- AE-B-C x 24 (86.14°, 45.82°, 48.03°)
- AE-E-J x 24 (80.57°, 48.01°, 51.42°)
- AF-H-L x 24 (78.24°, 49.42°, 52.34°)
- AF-I-U x 24 (75.32°, 49.28°, 55.40°)
- AG-E-K x 24 (82.20°, 47.22°, 50.58°)
- AG-H-R x 24 (77.79°, 48.31°, 53.90°)
- AH-N-S x 24 (75.30°, 51.28°, 53.42°)
- AH-O-Q x 24 (75.67°, 51.68°, 52.65°)
- AI-J-J x 8 (83.35°, 48.32°, 48.32°)
- AI-P-P x 8 (78.90°, 50.55°, 50.55°)
- AJ-J-J x 4 (83.41°, 48.30°, 48.30°)
- AJ-P-P x 4 (78.95°, 50.52°, 50.52°)
- AK-Q-W x 24 (76.41°, 50.16°, 53.42°)
- AL-S-X x 24 (76.41°, 50.54°, 53.04°)
- AL-T-U x 24 (77.75°, 51.01°, 51.24°)
- AM-P-R x 24 (80.50°, 49.28°, 50.22°)
- AM-T-V x 24 (77.47°, 50.22°, 52.31°)
- AN-Y-Y x 12 (77.54°, 51.23°, 51.23°)
- AO-W-Y x 24 (77.86°, 50.89°, 51.25°)
- AO-X-Z x 24 (77.48°, 50.88°, 51.64°)
- AP-V-V x 12 (78.88°, 50.56°, 50.56°)
- AP-Z-Z x 12 (77.55°, 51.23°, 51.23°)
- 30 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 0.995 or 49.75% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 7V Cube Dome (Human is 170cm/5'7")

Cuboctahedron

Uniform Polyhedron: U7
Archimedean Solid: A1
Vertices: 12
Edges: 24
Faces: 14
Wythoff symbol: 2|3 4
Symmetry Group: octahedral
Vertex Configuration: {3, 4, 3, 4}
Dual: rhombic dodecahedron
V: s³ * 5/3 * √2
A: s² * (6 + 2 * √3)
r_inner: s * 3/4
r_outer: s

Cuboctahedron L0/0V (original)

Cuboctahedron L1/1V flat (only triangles & flat)

Cuboctahedron L1/1V (only triangles & normalized)

The 6 squares are centerpoint triangulated for further processing.

Geodesic 1V Cuboctahedron Dome (front view)

Geodesic 1V Cuboctahedron Dome (bird view)

vertices/connectors: 12
- 9 x 4-way
- 3 x 6-way
1V Cuboctahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 12: 0.76537 (22.50°)
- B x 15: 1.00000 (30.00°)
- total 27 struts (2 kinds)¹⁾
- strut variance 30.7%
faces: 16 (3-sided)
- A-A-B x 12 (49.21°, 49.21°, 81.57°)
- B-B-B x 4 (60.00°, 60.00°, 60.00°)
- 2 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 0.817 or 40.83% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 1V Cuboctahedron Dome (Human is 170cm/5'7")

Geodesic 2V Cuboctahedron Dome (front view)

Geodesic 2V Cuboctahedron Dome (bird view)

vertices/connectors: 39
- 15 x 4-way
- 24 x 6-way
2V Cuboctahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 24: 0.39018 (11.25°)
- B x 24: 0.42291 (12.21°)
- C x 30: 0.51764 (15.00°)
- D x 12: 0.54120 (15.70°)
- E x 12: 0.57735 (16.78°)
- total 102 struts (5 kinds)¹⁾
- strut variance 48.0%
faces: 64 (3-sided)
- A-A-D x 12 (46.09°, 46.09°, 87.81°)
- A-B-C x 24 (47.72°, 53.31°, 78.96°)
- B-B-D x 12 (50.22°, 50.22°, 79.56°)
- C-C-E x 12 (56.10°, 56.10°, 67.80°)
- E-E-E x 4 (60.00°, 60.00°, 60.00°)
- 5 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 0.943 or 47.15% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 2V Cuboctahedron Dome (Human is 170cm/5'7")

There might be a better optimization available, but that's what I came up at the first sight.

Geodesic 3V Cuboctahedron Dome (front view)

Geodesic 3V Cuboctahedron Dome (bird view)

vertices/connectors: 82
- 21 x 4-way
- 61 x 6-way
3V Cuboctahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 24: 0.25480 (7.32°)
- B x 12: 0.27355 (7.86°)
- C x 24: 0.27468 (7.89°)
- D x 24: 0.27569 (7.92°)
- E x 24: 0.29082 (8.36°)
- F x 30: 0.33193 (9.55°)
- G x 12: 0.35741 (10.29°)
- H x 24: 0.36346 (10.47°)
- I x 27: 0.37796 (10.89°)
- J x 24: 0.38517 (11.10°)
- total 225 struts (10 kinds)¹⁾
- strut variance 51.2%
faces: 144 (3-sided)
- A-A-G x 12 (45.47°, 45.47°, 89.07°)
- A-D-F x 24 (48.51°, 54.14°, 77.35°)
- B-C-H x 24 (48.34°, 48.60°, 83.05°)
- C-C-G x 12 (49.42°, 49.42°, 81.16°)
- D-E-H x 24 (48.28°, 51.94°, 79.78°)
- E-E-I x 12 (49.46°, 49.46°, 81.07°)
- F-F-I x 12 (55.29°, 55.29°, 69.42°)
- I-J-J x 24 (58.77°, 60.62°, 60.62°)
- 8 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 3V Cuboctahedron Dome (Human is 170cm/5'7")

Geodesic 4V Cuboctahedron Dome (front view)

Geodesic 4V Cuboctahedron Dome (bird view)

vertices/connectors: 141
- 27 x 4-way
- 114 x 6-way
4V Cuboctahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 24: 0.18820 (5.40°)
- B x 24: 0.20036 (5.75°)
- C x 24: 0.20240 (5.81°)
- D x 24: 0.20386 (5.85°)
- E x 24: 0.20571 (5.90°)
- F x 24: 0.21338 (6.12°)
- G x 24: 0.21629 (6.21°)
- H x 24: 0.21961 (6.30°)
- I x 30: 0.24197 (6.95°)
- J x 24: 0.26458 (7.60°)
- K x 12: 0.26497 (7.61°)
- L x 24: 0.27316 (7.85°)
- M x 24: 0.27685 (7.96°)
- N x 12: 0.27735 (7.97°)
- O x 30: 0.28011 (8.05°)
- P x 12: 0.28580 (8.22°)
- Q x 24: 0.29180 (8.39°)
- R x 12: 0.30151 (8.67°)
- total 396 struts (18 kinds)¹⁾
- strut variance 60.2%
faces: 256 (3-sided)
- A-A-K x 12 (45.25°, 45.25°, 89.50°)
- A-C-I x 24 (49.12°, 54.41°, 76.47°)
- B-B-K x 12 (48.61°, 48.61°, 82.78°)
- B-D-L x 24 (46.95°, 48.03°, 85.02°)
- C-F-J x 24 (48.66°, 52.34°, 78.99°)
- D-E-J x 24 (49.46°, 50.06°, 80.48°)
- E-G-L x 24 (47.98°, 51.37°, 80.65°)
- F-H-O x 24 (48.73°, 50.67°, 80.60°)
- G-G-P x 12 (48.65°, 48.65°, 82.70°)
- H-H-P x 12 (49.40°, 49.40°, 81.19°)
- I-I-N x 12 (55.04°, 55.04°, 69.91°)
- M-M-N x 12 (59.94°, 59.94°, 60.12°)
- M-O-Q x 24 (57.85°, 58.95°, 63.19°)
- Q-Q-R x 12 (58.89°, 58.89°, 62.21°)
- R-R-R x 4 (60.00°, 60.00°, 60.00°)
- 15 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 0.985 or 49.24% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 4V Cuboctahedron Dome (Human is 170cm/5'7")

Geodesic L3 Cuboctahedron Dome (front view)

Geodesic L3 Cuboctahedron Dome (bird view)

vertices/connectors: 141
- 27 x 4-way
- 114 x 6-way
L3 Cuboctahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 48: 0.19603 (5.62°)
- B x 24: 0.19991 (5.74°)
- C x 24: 0.20044 (5.75°)
- D x 48: 0.21266 (6.10°)
- E x 24: 0.21671 (6.22°)
- F x 24: 0.21746 (6.24°)
- G x 60: 0.26105 (7.50°)
- H x 24: 0.26433 (7.59°)
- I x 24: 0.26899 (7.73°)
- J x 24: 0.27316 (7.85°)
- K x 12: 0.27590 (7.93°)
- L x 12: 0.27686 (7.96°)
- M x 24: 0.29180 (8.39°)
- N x 12: 0.29886 (8.59°)
- O x 12: 0.30151 (8.67°)
- total 396 struts (15 kinds)¹⁾
- strut variance 53.8%
faces: 256 (3-sided)
- A-A-K x 12 (45.27°, 45.27°, 89.47°)
- A-B-J x 24 (45.78°, 46.96°, 87.27°)
- A-D-H x 24 (47.00°, 52.53°, 80.47°)
- A-E-G x 24 (47.32°, 54.37°, 78.32°)
- B-B-K x 12 (46.36°, 46.36°, 87.28°)
- C-D-G x 24 (48.74°, 52.92°, 78.34°)
- C-E-H x 24 (48.00°, 53.47°, 78.53°)
- D-D-L x 12 (49.39°, 49.39°, 81.22°)
- D-F-J x 24 (49.80°, 51.36°, 78.84°)
- F-F-L x 12 (50.46°, 50.46°, 79.07°)
- G-G-N x 12 (55.08°, 55.08°, 69.83°)
- G-I-M x 24 (55.32°, 57.91°, 66.78°)
- I-I-N x 12 (56.25°, 56.25°, 67.50°)
- M-M-O x 12 (58.89°, 58.89°, 62.21°)
- O-O-O x 4 (60.00°, 60.00°, 60.00°)
- 15 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 0.985 or 49.24% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic L3 Cuboctahedron Dome (Human is 170cm/5'7")

Geodesic 5V Cuboctahedron Dome (front view)

Geodesic 5V Cuboctahedron Dome (bird view)

vertices/connectors: 216
- 33 x 4-way
- 183 x 6-way
5V Cuboctahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 24: 0.14897 (4.27°)
- B x 24: 0.15701 (4.50°)
- C x 24: 0.15942 (4.57°)
- D x 24: 0.16077 (4.61°)
- E x 24: 0.16199 (4.65°)
- F x 24: 0.16287 (4.67°)
- G x 12: 0.16512 (4.74°)
- H x 24: 0.16655 (4.78°)
- I x 24: 0.16939 (4.86°)
- J x 24: 0.17295 (4.96°)
- K x 24: 0.17327 (4.97°)
- L x 24: 0.17393 (4.99°)
- M x 24: 0.17615 (5.05°)
- N x 30: 0.18984 (5.45°)
- O x 24: 0.20577 (5.91°)
- P x 12: 0.21009 (6.03°)
- Q x 24: 0.21329 (6.12°)
- R x 24: 0.21561 (6.19°)
- S x 24: 0.21702 (6.23°)
- T x 30: 0.21808 (6.26°)
- U x 12: 0.21822 (6.26°)
- V x 12: 0.22654 (6.50°)
- W x 24: 0.22702 (6.52°)
- X x 24: 0.22923 (6.58°)
- Y x 15: 0.22942 (6.59°)
- Z x 24: 0.23096 (6.63°)
- AA x 24: 0.23738 (6.82°)
- AB x 12: 0.24254 (6.97°)
- total 615 struts (28 kinds)¹⁾
- strut variance 62.8%
faces: 400 (3-sided)
- A-A-P x 12 (45.17°, 45.17°, 89.66°)
- A-C-N x 24 (49.58°, 54.54°, 75.88°)
- AA-AA-AB x 12 (59.29°, 59.29°, 61.43°)
- AA-X-Z x 24 (62.11°, 58.57°, 59.32°)
- AB-AB-AB x 4 (60.00°, 60.00°, 60.00°)
- B-B-P x 12 (48.00°, 48.00°, 84.00°)
- B-D-S x 24 (46.21°, 47.67°, 86.12°)
- C-H-O x 24 (49.32°, 52.43°, 78.26°)
- D-F-O x 24 (50.07°, 50.98°, 78.95°)
- E-G-R x 24 (48.15°, 49.39°, 82.46°)
- E-I-S x 24 (47.63°, 50.59°, 81.78°)
- F-J-R x 24 (48.05°, 52.12°, 79.83°)
- H-K-T x 24 (48.75°, 51.45°, 79.80°)
- I-I-V x 12 (48.05°, 48.05°, 83.91°)
- J-L-W x 24 (48.92°, 49.31°, 81.77°)
- K-M-W x 24 (48.94°, 50.06°, 81.00°)
- L-L-V x 12 (49.37°, 49.37°, 81.27°)
- M-M-Y x 12 (49.39°, 49.39°, 81.23°)
- N-N-U x 12 (54.91°, 54.91°, 70.17°)
- Q-Q-U x 12 (59.24°, 59.24°, 61.53°)
- Q-T-Z x 24 (56.62°, 58.64°, 64.74°)
- X-X-Y x 12 (59.97°, 59.97°, 60.06°)
- 22 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 0.990 or 49.51% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 5V Cuboctahedron Dome (Human is 170cm/5'7")

Geodesic 6V Cuboctahedron Dome (front view)

Geodesic 6V Cuboctahedron Dome (bird view)

vertices/connectors: 307
- 39 x 4-way
- 268 x 6-way
6V Cuboctahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 24: 0.12319 (3.53°)
- B x 24: 0.12886 (3.69°)
- C x 24: 0.13134 (3.77°)
- D x 24: 0.13213 (3.79°)
- E x 24: 0.13294 (3.81°)
- F x 24: 0.13429 (3.85°)
- G x 24: 0.13485 (3.87°)
- H x 24: 0.13595 (3.90°)
- I x 24: 0.13710 (3.93°)
- J x 24: 0.13831 (3.97°)
- K x 24: 0.14205 (4.07°)
- L x 24: 0.14228 (4.08°)
- M x 24: 0.14239 (4.08°)
- N x 24: 0.14313 (4.10°)
- O x 24: 0.14372 (4.12°)
- P x 24: 0.14489 (4.15°)
- Q x 24: 0.14671 (4.21°)
- R x 24: 0.14719 (4.22°)
- S x 30: 0.15602 (4.47°)
- T x 24: 0.16762 (4.81°)
- U x 24: 0.17260 (4.95°)
- V x 12: 0.17389 (4.99°)
- W x 24: 0.17620 (5.05°)
- X x 30: 0.17706 (5.08°)
- Y x 24: 0.17943 (5.15°)
- Z x 12: 0.17961 (5.15°)
- AA x 24: 0.18035 (5.17°)
- AB x 24: 0.18541 (5.32°)
- AC x 24: 0.18597 (5.34°)
- AD x 12: 0.18657 (5.35°)
- AE x 24: 0.18878 (5.42°)
- AF x 54: 0.18984 (5.45°)
- AG x 12: 0.19220 (5.51°)
- AH x 48: 0.19238 (5.52°)
- AI x 24: 0.20000 (5.74°)
- AJ x 24: 0.20102 (5.77°)
- total 882 struts (36 kinds)¹⁾
- strut variance 63.1%
faces: 576 (3-sided)
- A-A-V x 12 (45.11°, 45.11°, 89.78°)
- A-C-S x 24 (49.88°, 54.59°, 75.53°)
- AA-E-I x 24 (83.83°, 47.09°, 49.08°)
- AA-G-N x 24 (80.90°, 47.55°, 51.56°)
- AB-K-P x 24 (80.47°, 49.10°, 50.42°)
- AB-L-O x 24 (80.82°, 49.26°, 49.92°)
- AC-AF-AH x 48 (58.24°, 60.18°, 61.58°)
- AD-J-J x 12 (84.85°, 47.58°, 47.58°)
- AD-M-M x 12 (81.87°, 49.07°, 49.07°)
- AE-M-N x 24 (82.80°, 48.44°, 48.76°)
- AE-O-Q x 24 (81.10°, 48.76°, 50.14°)
- AF-P-R x 24 (81.05°, 48.95°, 50.01°)
- AF-U-X x 24 (65.73°, 56.00°, 58.28°)
- AG-Q-Q x 12 (81.85°, 49.07°, 49.07°)
- AG-R-R x 12 (81.51°, 49.24°, 49.24°)
- AH-AH-AI x 24 (58.68°, 58.68°, 62.63°)
- AI-AJ-AJ x 24 (59.67°, 60.16°, 60.16°)
- B-B-V x 12 (47.58°, 47.58°, 84.84°)
- B-D-Y x 24 (45.84°, 47.33°, 86.83°)
- C-H-T x 24 (49.94°, 52.39°, 77.67°)
- D-F-T x 24 (50.43°, 51.60°, 77.97°)
- E-J-Y x 24 (47.30°, 49.89°, 82.80°)
- F-L-W x 24 (48.45°, 52.47°, 79.08°)
- G-I-W x 24 (49.04°, 50.18°, 80.78°)
- H-K-X x 24 (48.90°, 51.99°, 79.11°)
- S-S-Z x 12 (54.86°, 54.86°, 70.29°)
- U-U-Z x 12 (58.65°, 58.65°, 62.70°)
- 27 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 6V Cuboctahedron Dome (Human is 170cm/5'7")

Geodesic 2V.3V Cuboctahedron Dome (front view)

Geodesic 2V.3V Cuboctahedron Dome (bird view)

vertices/connectors: 307
- 39 x 4-way
- 268 x 6-way
2V.3V Cuboctahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 48: 0.13005 (3.73°)
- B x 48: 0.13235 (3.79°)
- C x 24: 0.13239 (3.80°)
- D x 24: 0.13292 (3.81°)
- E x 24: 0.13301 (3.81°)
- F x 24: 0.13431 (3.85°)
- G x 24: 0.13456 (3.86°)
- H x 48: 0.14095 (4.04°)
- I x 24: 0.14363 (4.12°)
- J x 24: 0.14376 (4.12°)
- K x 24: 0.14386 (4.12°)
- L x 24: 0.14407 (4.13°)
- M x 24: 0.14420 (4.13°)
- N x 24: 0.14559 (4.17°)
- O x 24: 0.14602 (4.19°)
- P x 60: 0.17250 (4.95°)
- Q x 24: 0.17578 (5.04°)
- R x 24: 0.17622 (5.05°)
- S x 24: 0.17677 (5.07°)
- T x 30: 0.17792 (5.10°)
- U x 24: 0.17845 (5.12°)
- V x 24: 0.17859 (5.12°)
- W x 24: 0.18000 (5.16°)
- X x 24: 0.18035 (5.17°)
- Y x 12: 0.18353 (5.27°)
- Z x 12: 0.18409 (5.28°)
- AA x 24: 0.18431 (5.29°)
- AB x 24: 0.18489 (5.30°)
- AC x 12: 0.18657 (5.35°)
- AD x 24: 0.19238 (5.52°)
- AE x 12: 0.19845 (5.69°)
- AF x 24: 0.19944 (5.72°)
- AG x 24: 0.20000 (5.74°)
- AH x 24: 0.20102 (5.77°)
- total 882 struts (34 kinds)¹⁾
- strut variance 54.6%
faces: 576 (3-sided)
- A-A-Y x 12 (45.11°, 45.11°, 89.78°)
- A-C-X x 24 (46.02°, 47.12°, 86.86°)
- A-H-Q x 24 (46.89°, 52.30°, 80.82°)
- A-J-P x 24 (47.47°, 54.60°, 77.92°)
- AA-B-B x 24 (88.30°, 45.85°, 45.85°)
- AA-C-G x 24 (87.30°, 45.86°, 46.85°)
- AB-K-L x 24 (79.88°, 50.01°, 50.11°)
- AB-M-O x 24 (79.16°, 49.99°, 50.85°)
- AC-G-G x 12 (87.76°, 46.12°, 46.12°)
- AC-O-O x 12 (79.44°, 50.28°, 50.28°)
- AD-AD-AG x 12 (58.68°, 58.68°, 62.63°)
- AD-P-U x 24 (66.48°, 55.29°, 58.23°)
- AE-P-P x 12 (70.21°, 54.90°, 54.90°)
- AE-V-V x 12 (67.48°, 56.26°, 56.26°)
- AF-T-V x 24 (68.02°, 55.82°, 56.16°)
- AF-U-W x 24 (67.61°, 55.81°, 56.58°)
- AG-AH-AH x 24 (59.67°, 60.16°, 60.16°)
- AG-W-W x 12 (67.50°, 56.25°, 56.25°)
- B-B-Y x 12 (46.09°, 46.09°, 87.82°)
- B-I-R x 24 (47.54°, 53.20°, 79.26°)
- D-I-Q x 24 (47.88°, 53.27°, 78.86°)
- D-K-S x 24 (47.61°, 53.10°, 79.28°)
- E-H-P x 24 (48.96°, 53.03°, 78.01°)
- E-N-S x 24 (47.52°, 53.84°, 78.64°)
- F-J-R x 24 (48.33°, 53.12°, 78.55°)
- F-N-T x 24 (47.78°, 53.41°, 78.81°)
- H-H-Z x 12 (49.21°, 49.21°, 81.58°)
- H-M-X x 24 (49.94°, 51.56°, 78.50°)
- L-L-Z x 12 (50.30°, 50.30°, 79.40°)
- 29 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 2V.3V Cuboctahedron Dome (Human is 170cm/5'7")

Geodesic 3V.2V Cuboctahedron Dome (front view)

Geodesic 3V.2V Cuboctahedron Dome (bird view)

vertices/connectors: 307
- 39 x 4-way
- 268 x 6-way
3V.2V Cuboctahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 48: 0.12766 (3.66°)
- B x 24: 0.12871 (3.69°)
- C x 24: 0.12884 (3.69°)
- D x 24: 0.13710 (3.93°)
- E x 48: 0.13767 (3.95°)
- F x 48: 0.13817 (3.96°)
- G x 24: 0.13839 (3.97°)
- H x 48: 0.13896 (3.98°)
- I x 24: 0.13926 (3.99°)
- J x 24: 0.13962 (4.00°)
- K x 48: 0.14580 (4.18°)
- L x 24: 0.14716 (4.22°)
- M x 24: 0.14733 (4.22°)
- N x 60: 0.16654 (4.78°)
- O x 24: 0.16744 (4.80°)
- P x 24: 0.16860 (4.84°)
- Q x 24: 0.17943 (5.15°)
- R x 12: 0.18017 (5.17°)
- S x 12: 0.18041 (5.18°)
- T x 48: 0.18249 (5.24°)
- U x 24: 0.18346 (5.26°)
- V x 24: 0.18358 (5.27°)
- W x 54: 0.18984 (5.45°)
- X x 12: 0.19101 (5.48°)
- Y x 12: 0.19164 (5.50°)
- Z x 24: 0.19259 (5.53°)
- AA x 48: 0.19350 (5.55°)
- AB x 48: 0.19619 (5.63°)
- total 882 struts (28 kinds)¹⁾
- strut variance 53.6%
faces: 576 (3-sided)
- A-A-R x 12 (45.13°, 45.13°, 89.75°)
- A-B-Q x 24 (45.37°, 45.83°, 88.80°)
- A-F-O x 24 (48.24°, 53.83°, 77.92°)
- A-I-N x 24 (48.36°, 54.61°, 77.02°)
- AA-AA-Z x 24 (60.15°, 60.15°, 59.69°)
- AA-AB-W x 48 (60.14°, 61.57°, 58.29°)
- AB-AB-Z x 24 (60.61°, 60.61°, 58.79°)
- B-B-R x 12 (45.57°, 45.57°, 88.87°)
- C-F-N x 24 (48.93°, 54.00°, 77.07°)
- C-I-O x 24 (48.61°, 54.23°, 77.17°)
- D-E-U x 24 (47.97°, 48.25°, 83.79°)
- D-H-T x 24 (48.18°, 49.07°, 82.75°)
- E-E-S x 12 (49.08°, 49.08°, 81.85°)
- E-G-T x 24 (48.46°, 48.79°, 82.75°)
- E-H-Q x 24 (49.27°, 49.90°, 80.83°)
- F-K-V x 24 (47.94°, 51.56°, 80.50°)
- F-L-T x 24 (48.11°, 52.46°, 79.43°)
- G-H-U x 24 (48.45°, 48.73°, 82.83°)
- H-H-S x 12 (49.54°, 49.54°, 80.92°)
- J-K-T x 24 (48.77°, 51.76°, 79.47°)
- J-L-V x 24 (48.40°, 52.04°, 79.56°)
- K-K-X x 12 (49.08°, 49.08°, 81.84°)
- K-M-W x 24 (49.30°, 49.99°, 80.71°)
- M-M-X x 12 (49.58°, 49.58°, 80.83°)
- N-N-Y x 12 (54.87°, 54.87°, 70.25°)
- N-P-W x 24 (54.98°, 56.02°, 69.00°)
- P-P-Y x 12 (55.37°, 55.37°, 69.25°)
- 27 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 3V.2V Cuboctahedron Dome (Human is 170cm/5'7")

Truncated Octahedron

Uniform Polyhedron: U8
Archimedean Solid: A12
Vertices: 24
Edges: 36
Faces: 14
Wythoff symbol: 2 4|3
Symmetry Group: octahedral
Vertex Configuration: {6, 6, 4}
Dual: tetrakis hexahedron
V: s³ * 8 * √2
A: s² * (6 + 12 * √3)
r_inner: s * 9/20 * √10
r_outer: s / 2 * √10

Truncated Octahedron L0/0V (original)

Truncated Octahedron L1/1V flat (only triangles & flat)

Truncated Octahedron L1/1V (only triangles & normalized)

The 8 hexagons and 6 squares are centerpoint triangulated for further processing.

Geodesic 1V Truncated Octahedron Dome (front view)

Geodesic 1V Truncated Octahedron Dome (bird view)

vertices/connectors: 25
- 4 x 3-way
- 9 x 4-way
- 12 x 6-way
1V Truncated Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 16: 0.45951 (13.28°)
- B x 2: 0.63245 (18.43°)
- C x 18: 0.63246 (18.44°)
- D x 24: 0.67142 (19.62°)
- total 60 struts (4 kinds)¹⁾
- strut variance 46.1%
faces: 36 (3-sided)
- A-A-C x 12 (46.51°, 46.51°, 86.98°)
- B-D-D x 2 (56.19°, 61.90°, 61.90°)
- C-D-D x 22 (56.20°, 61.90°, 61.90°)
- 3 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 1V Truncated Octahedron Dome (Human is 170cm/5'7")

Geodesic 2V Truncated Octahedron Dome (front view)

Geodesic 2V Truncated Octahedron Dome (bird view)

vertices/connectors: 85
- 4 x 3-way
- 21 x 4-way
- 60 x 6-way
2V Truncated Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 32: 0.23131 (6.64°)
- B x 24: 0.23773 (6.83°)
- C x 40: 0.32036 (9.22°)
- D x 12: 0.32492 (9.35°)
- E x 24: 0.33571 (9.66°)
- F x 48: 0.34069 (9.81°)
- G x 48: 0.35506 (10.23°)
- total 228 struts (7 kinds)¹⁾
- strut variance 53.5%
faces: 144 (3-sided)
- A-A-D x 12 (45.39°, 45.39°, 89.23°)
- A-B-C x 24 (46.08°, 47.75°, 86.17°)
- B-B-D x 12 (46.89°, 46.89°, 86.22°)
- C-F-G x 48 (54.79°, 60.32°, 64.89°)
- E-F-F x 24 (59.03°, 60.48°, 60.48°)
- E-G-G x 24 (56.42°, 61.79°, 61.79°)
- 6 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 2V Truncated Octahedron Dome (Human is 170cm/5'7")

Geodesic 3V Truncated Octahedron Dome (front view)

Geodesic 3V Truncated Octahedron Dome (bird view)

vertices/connectors: 181
- 4 x 3-way
- 33 x 4-way
- 144 x 6-way
3V Truncated Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 32: 0.15315 (4.39°)
- B x 16: 0.15689 (4.50°)
- C x 24: 0.15697 (4.50°)
- D x 24: 0.15706 (4.50°)
- E x 24: 0.16057 (4.60°)
- F x 40: 0.21070 (6.05°)
- G x 12: 0.21595 (6.20°)
- H x 24: 0.21723 (6.24°)
- I x 20: 0.22086 (6.34°)
- J x 24: 0.22224 (6.38°)
- K x 96: 0.22365 (6.42°)
- L x 48: 0.23512 (6.75°)
- M x 24: 0.23594 (6.77°)
- N x 48: 0.23610 (6.78°)
- O x 48: 0.23760 (6.82°)
- total 504 struts (15 kinds)¹⁾
- strut variance 55.1%
faces: 324 (3-sided)
- A-A-G x 12 (45.17°, 45.17°, 89.65°)
- A-D-F x 24 (46.46°, 48.02°, 85.52°)
- B-C-H x 24 (46.20°, 46.24°, 87.57°)
- C-C-G x 12 (46.54°, 46.54°, 86.93°)
- D-E-H x 24 (46.20°, 47.55°, 86.25°)
- E-E-I x 12 (46.55°, 46.55°, 86.90°)
- F-K-L x 48 (54.62°, 59.91°, 65.47°)
- I-N-N x 24 (55.78°, 62.11°, 62.11°)
- J-K-K x 24 (59.59°, 60.21°, 60.21°)
- J-O-O x 24 (55.76°, 62.12°, 62.12°)
- K-L-N x 48 (56.66°, 61.45°, 61.90°)
- K-M-O x 48 (56.36°, 61.44°, 62.21°)
- 12 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 3V Truncated Octahedron Dome (Human is 170cm/5'7")

Geodesic 4V Truncated Octahedron Dome (front view)

Geodesic 4V Truncated Octahedron Dome (bird view)

vertices/connectors: 313
- 4 x 3-way
- 45 x 4-way
- 264 x 6-way
4V Truncated Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 32: 0.11427 (3.28°)
- B x 24: 0.11666 (3.34°)
- C x 24: 0.11683 (3.35°)
- D x 32: 0.11742 (3.37°)
- E x 24: 0.11755 (3.37°)
- F x 24: 0.11965 (3.43°)
- G x 24: 0.11984 (3.44°)
- H x 24: 0.12061 (3.46°)
- I x 40: 0.15644 (4.49°)
- J x 36: 0.16131 (4.63°)
- K x 24: 0.16300 (4.67°)
- L x 40: 0.16496 (4.73°)
- M x 48: 0.16522 (4.74°)
- N x 24: 0.16525 (4.74°)
- O x 12: 0.16571 (4.75°)
- P x 48: 0.16582 (4.76°)
- Q x 48: 0.16845 (4.83°)
- R x 24: 0.16996 (4.87°)
- S x 48: 0.17431 (5.00°)
- T x 48: 0.17490 (5.02°)
- U x 48: 0.17555 (5.04°)
- V x 48: 0.17612 (5.05°)
- W x 48: 0.17760 (5.09°)
- X x 48: 0.17888 (5.13°)
- Y x 48: 0.18059 (5.18°)
- total 888 struts (25 kinds)¹⁾
- strut variance 58.0%
faces: 576 (3-sided)
- A-A-J x 12 (45.12°, 45.12°, 89.76°)
- A-C-I x 24 (46.74°, 48.09°, 85.18°)
- B-B-J x 12 (46.28°, 46.28°, 87.43°)
- B-D-K x 24 (45.69°, 46.05°, 88.26°)
- C-F-J x 24 (46.25°, 47.76°, 86.00°)
- D-E-J x 24 (46.60°, 46.71°, 86.69°)
- E-G-K x 24 (46.08°, 47.20°, 86.72°)
- F-H-L x 24 (46.41°, 46.86°, 86.73°)
- G-G-O x 12 (46.25°, 46.25°, 87.51°)
- H-H-O x 12 (46.61°, 46.61°, 86.78°)
- I-P-T x 48 (54.57°, 59.75°, 65.68°)
- L-S-W x 48 (55.91°, 61.03°, 63.06°)
- M-S-T x 48 (56.47°, 61.58°, 61.95°)
- M-V-X x 48 (55.46°, 61.41°, 63.13°)
- N-P-P x 24 (59.80°, 60.10°, 60.10°)
- N-U-U x 24 (56.16°, 61.92°, 61.92°)
- Q-U-V x 48 (57.22°, 61.24°, 61.54°)
- Q-X-Y x 48 (55.86°, 61.56°, 62.58°)
- R-W-W x 24 (57.19°, 61.41°, 61.41°)
- R-Y-Y x 24 (56.15°, 61.92°, 61.92°)
- 20 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 4V Truncated Octahedron Dome (Human is 170cm/5'7")

Geodesic L3 Truncated Octahedron Dome (front view)

Geodesic L3 Truncated Octahedron Dome (bird view)

vertices/connectors: 313
- 4 x 3-way
- 45 x 4-way
- 264 x 6-way
L3 Truncated Octahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 64: 0.11585 (3.32°)
- B x 24: 0.11663 (3.34°)
- C x 24: 0.11667 (3.34°)
- D x 48: 0.11908 (3.41°)
- E x 48: 0.11988 (3.44°)
- F x 80: 0.16070 (4.61°)
- G x 24: 0.16129 (4.63°)
- H x 48: 0.16266 (4.67°)
- I x 24: 0.16300 (4.67°)
- J x 24: 0.16362 (4.69°)
- K x 48: 0.16845 (4.83°)
- L x 6: 0.17034 (4.89°)
- M x 18: 0.17035 (4.89°)
- N x 24: 0.17056 (4.89°)
- O x 96: 0.17097 (4.90°)
- P x 96: 0.17281 (4.96°)
- Q x 96: 0.17824 (5.11°)
- R x 48: 0.18000 (5.16°)
- S x 48: 0.18023 (5.17°)
- total 888 struts (19 kinds)¹⁾
- strut variance 55.6%
faces: 576 (3-sided)
- A-A-J x 12 (45.06°, 45.06°, 89.88°)
- A-B-I x 24 (45.26°, 45.66°, 89.07°)
- A-D-G x 24 (45.79°, 47.49°, 86.72°)
- A-E-F x 24 (45.96°, 48.09°, 85.95°)
- B-B-J x 12 (45.45°, 45.45°, 89.10°)
- C-D-F x 24 (46.42°, 47.67°, 85.92°)
- C-E-G x 24 (46.19°, 47.86°, 85.95°)
- D-D-J x 12 (46.62°, 46.62°, 86.76°)
- D-E-I x 24 (46.79°, 47.21°, 86.00°)
- E-E-J x 12 (46.98°, 46.98°, 86.04°)
- F-O-R x 48 (54.42°, 59.93°, 65.64°)
- F-P-Q x 48 (54.47°, 61.05°, 64.48°)
- H-O-Q x 48 (55.49°, 60.01°, 64.50°)
- H-P-R x 48 (54.88°, 60.31°, 64.81°)
- K-O-P x 48 (58.65°, 60.14°, 61.21°)
- K-Q-S x 48 (56.05°, 61.38°, 62.58°)
- L-O-O x 6 (59.73°, 60.14°, 60.14°)
- L-P-P x 6 (59.05°, 60.48°, 60.48°)
- M-O-O x 18 (59.77°, 60.12°, 60.12°)
- M-P-P x 18 (59.08°, 60.46°, 60.46°)
- N-Q-Q x 24 (57.20°, 61.40°, 61.40°)
- N-S-S x 24 (56.51°, 61.75°, 61.75°)
- 22 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.000 or 50.00% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic L3 Truncated Octahedron Dome (Human is 170cm/5'7")

Rhombicuboctahedron

Uniform Polyhedron: U10
aka Small Rhombicuboctahedron
Archimedean Solid: A6
Vertices: 24
Edges: 48
Faces: 26
Wythoff symbol: 3 4|2
Symmetry Group: octahedral
Vertex Configuration: {4, 3, 4, 4}
Dual: deltoidal icositetrahedron
V: s³ / 3 * (12 + 10 * √2)
A: s² * (18 + 2 * √3)
r_inner: s / 17 * (6 + √2) * √(5 + 2 * √2)
r_outer: s / 2 * √(5 + 2 * √2)

Rhombicuboctahedron L0/0V (original)

Rhombicuboctahedron L1/1V flat (only triangles & flat)

Rhombicuboctahedron L1/1V (only triangles & normalized)

The squares are triangulated for further processing.

Geodesic 1V 3/8 Rhombicuboctahedron Dome (front view)

Geodesic 1V 3/8 Rhombicuboctahedron Dome (bird view)

vertices/connectors: 17
- 13 x 4-way
- 4 x 7-way
1V 3/8 Rhombicuboctahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 20: 0.52372 (15.18°)
- B x 20: 0.71481 (20.94°)
- total 40 struts (2 kinds)¹⁾
- strut variance 36.5%
faces: 24 (3-sided)
- A-A-B x 20 (46.96°, 46.96°, 86.07°)
- B-B-B x 4 (60.00°, 60.00°, 60.00°)
- 2 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 0.643 or 32.14% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 1V 3/8 Rhombicuboctahedron Dome (Human is 170cm/5'7")

Geodesic 1V 5/8 Rhombicuboctahedron Dome (front view)

Geodesic 1V 5/8 Rhombicuboctahedron Dome (bird view)

vertices/connectors: 33
- 13 x 4-way
- 8 x 5-way
- 12 x 7-way
1V 5/8 Rhombicuboctahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 52: 0.52372 (15.18°)
- B x 36: 0.71481 (20.94°)
- total 88 struts (2 kinds)¹⁾
- strut variance 36.5%
faces: 56 (3-sided)
- A-A-B x 52 (46.96°, 46.96°, 86.07°)
- B-B-B x 4 (60.00°, 60.00°, 60.00°)
- 2 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.358 or 67.88% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 1V 5/8 Rhombicuboctahedron Dome (Human is 170cm/5'7")

This is a nice variant, with square walls, optionally instead of square triangulation either replaced by one strut (B * √2) or leave it out at all.

The vertical struts of the vertical wall make it look very artistic, yet also edgy, but given it's a 1V it's understandable. With only 88 struts you get a 5/8 sphere.

At d = 6m the height is apprx. 4m and a 2nd level can be done at 2m height, just at the level of existing connectors.

Geodesic 2V 3/8 Rhombicuboctahedron Dome (front view)

Geodesic 2V 3/8 Rhombicuboctahedron Dome (bird view)

vertices/connectors: 57
- 21 x 4-way
- 32 x 6-way
- 4 x 7-way
2V 3/8 Rhombicuboctahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 40: 0.26418 (7.59°)
- B x 40: 0.27386 (7.87°)
- C x 40: 0.36346 (10.47°)
- D x 20: 0.37033 (10.67°)
- E x 12: 0.38268 (11.03°)
- total 152 struts (5 kinds)¹⁾
- strut variance 44.9%
faces: 96 (3-sided)
- A-A-D x 20 (45.51°, 45.51°, 88.98°)
- A-B-C x 40 (46.39°, 48.64°, 84.97°)
- B-B-D x 20 (47.47°, 47.47°, 85.06°)
- C-C-E x 12 (58.24°, 58.24°, 63.53°)
- E-E-E x 4 (60.00°, 60.00°, 60.00°)
- 5 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 0.643 or 32.14% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 2V 3/8 Rhombicuboctahedron Dome (Human is 170cm/5'7")

Geodesic 2V 5/8 Rhombicuboctahedron Dome (front view)

Geodesic 2V 5/8 Rhombicuboctahedron Dome (bird view)

vertices/connectors: 121
- 21 x 4-way
- 8 x 5-way
- 80 x 6-way
- 12 x 7-way
2V 5/8 Rhombicuboctahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 104: 0.26418 (7.59°)
- B x 104: 0.27386 (7.87°)
- C x 72: 0.36346 (10.47°)
- D x 52: 0.37033 (10.67°)
- E x 12: 0.38268 (11.03°)
- total 344 struts (5 kinds)¹⁾
- strut variance 44.9%
faces: 224 (3-sided)
- A-A-D x 52 (45.51°, 45.51°, 88.98°)
- A-B-C x 104 (46.39°, 48.64°, 84.97°)
- B-B-D x 52 (47.47°, 47.47°, 85.06°)
- C-C-E x 12 (58.24°, 58.24°, 63.53°)
- E-E-E x 4 (60.00°, 60.00°, 60.00°)
- 5 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.383 or 69.14% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 2V 5/8 Rhombicuboctahedron Dome (Human is 170cm/5'7")

This is also a nice variant, alike the 1V 5/8 one. Multiple squares in a spherical setting, a nice crossover of rectangular to circular/spherical space.

With 344 struts still considerable for temporary buildings.

Geodesic 3V 3/8 Rhombicuboctahedron Dome (front view)

Geodesic 3V 3/8 Rhombicuboctahedron Dome (bird view)

vertices/connectors: 121
- 29 x 4-way
- 88 x 6-way
- 4 x 7-way
3V 3/8 Rhombicuboctahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 40: 0.17453 (5.01°)
- B x 20: 0.18015 (5.17°)
- C x 40: 0.18031 (5.17°)
- D x 40: 0.18048 (5.18°)
- E x 40: 0.18562 (5.33°)
- F x 40: 0.23805 (6.84°)
- G x 20: 0.24588 (7.06°)
- H x 40: 0.24779 (7.12°)
- I x 32: 0.25307 (7.27°)
- J x 24: 0.25516 (7.33°)
- total 336 struts (10 kinds)¹⁾
- strut variance 46.2%
faces: 216 (3-sided)
- A-A-G x 20 (45.20°, 45.20°, 89.59°)
- A-D-F x 40 (46.82°, 48.96°, 84.22°)
- B-C-H x 40 (46.56°, 46.59°, 86.85°)
- C-C-G x 20 (47.01°, 47.01°, 85.99°)
- D-E-H x 40 (46.54°, 48.28°, 85.19°)
- E-E-I x 20 (47.01°, 47.01°, 85.98°)
- F-F-I x 12 (57.89°, 57.89°, 64.21°)
- I-J-J x 24 (59.46°, 60.27°, 60.27°)
- 8 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 0.643 or 32.14% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 3V 3/8 Rhombicuboctahedron Dome (Human is 170cm/5'7")

Geodesic 3V 5/8 Rhombicuboctahedron Dome (front view)

Geodesic 3V 5/8 Rhombicuboctahedron Dome (bird view)

vertices/connectors: 265
- 29 x 4-way
- 8 x 5-way
- 216 x 6-way
- 12 x 7-way
3V 5/8 Rhombicuboctahedron Dome Construction Map
edges/struts & bending angles (α_strut):
- A x 104: 0.17453 (5.01°)
- B x 52: 0.18015 (5.17°)
- C x 104: 0.18031 (5.17°)
- D x 104: 0.18048 (5.18°)
- E x 104: 0.18562 (5.33°)
- F x 72: 0.23805 (6.84°)
- G x 52: 0.24588 (7.06°)
- H x 104: 0.24779 (7.12°)
- I x 48: 0.25307 (7.27°)
- J x 24: 0.25516 (7.33°)
- total 768 struts (10 kinds)¹⁾
- strut variance 46.2%
faces: 504 (3-sided)
- A-A-G x 52 (45.20°, 45.20°, 89.59°)
- A-D-F x 104 (46.82°, 48.96°, 84.22°)
- B-C-H x 104 (46.56°, 46.59°, 86.85°)
- C-C-G x 52 (47.01°, 47.01°, 85.99°)
- D-E-H x 104 (46.54°, 48.28°, 85.19°)
- E-E-I x 52 (47.01°, 47.01°, 85.98°)
- F-F-I x 12 (57.89°, 57.89°, 64.21°)
- I-J-J x 24 (59.46°, 60.27°, 60.27°)
- 8 kinds of faces²⁾
diameter: 2.000, radius: 1.000
height: 1.380 or 68.99% of diameter

1) strut lengths sorted by 1/10'000th or +/-0.00005 exact
2) clock wise (cw) and counter clock wise (ccw) orientation neglected

Geodesic 3V 5/8 Rhombicuboctahedron Dome (Human is 170cm/5'7")

Building a model I think is very useful, you are getting an impression of the overall overhead, struts, connectors and even sewing the cover. Yet, a model cannot replace thorough investigation of the actual method and construction; I tend to make small tests in actual size for critical parts of a construction.

Anyway, I made a couple of geodesic models, four of them I include here in more details. Please note, the notion of the strut types (lengths) A-F for 2V, 3V and the 4V Icosahedron models do not match the ones I listed previously, the strut notion for the models are those from DesertDomes.com which I used in previous version of these notes. In case you also used a different notion, you can easily map them to my notion, just compare the values, they are numerically the same, just the notion of A, B, C etc are different.

3V 5/9 Dome, build with bamboo sticks and PVC pipe as junction
In order to explore the form deeper, I thought to start with a model - using easy available material like bamboo sticks from a garden shop. Other web-sites have some suggestions about building a model using PVC pipe as junction between dome struts, and this what I did then.

So, I bought

150 bamboo sticks (10 packages a 15 sticks), 4mm diameter, 40cm long, and
9m PVC pipe outer diameter 6mm, inner diameter 4mm

Cost CHF 18, € 12 or US$15. I used the 3V 5/9 calculator entered A_lath+B_lath+C_lath = 40cm, and l_hole = 0.5cm, and got my A_lath, B_lath and C_lath to cut.

r = 37cm, d = 74cm
A = 11.9cm (x 60)
B = 13.9cm (x 90)
C = 14.2cm (x 120)

so I actually cut for a full sphere, whereas the 3V 5/9 sphere only requires A x 30, B x 55, C x 80. Following cuts I made:

90x B+C
30x A+C
15x A+A

Step by Step

The material: bamboo sticks (40cm x 4mm, 150 pieces), PVC pipe (9m), cord
2005/08/30 12:27

2005/08/30 12:27

PVC junction, 1cm for each stick, 0.5cm junction = 3cm length
2005/08/30 12:27

6-way junction test
2005/08/30 12:27

2005/08/30 12:27

2005/08/30 12:28

My choice to bind it
2005/08/30 12:28

Preparing the cut of A, B, and C
2005/08/30 12:28

60x A, 90x B, 120x C
2005/08/30 12:28

All PVC cut
2005/08/30 12:28

The knot, step 1
2005/08/30 12:28

The knot, step 2
2005/08/30 12:28

The knot, step 3
2005/08/30 12:28

The knot, step 4
2005/08/30 12:29

Another approach to bind the PVC pipe, easier than with a cord
2006/02/04 18:00

A couple of junctions (all 6-way)
2005/08/30 12:29

3V 3/8 Dome
2005/08/30 12:29

3V 5/8 Dome
2005/08/30 12:29

2005/08/30 12:29

As considered I used the left-over of the 3V and some spare sticks to build a 2V 4/8 Sphere:

r = 18.3cm, d = 36.6cm
A = 11.4cm (x 35)
B = 10.0cm (x 30)

2V 4/8 Dome
2005/08/30 17:41

2005/08/30 17:41

2V 4/8 Dome within a 3V 5/8 Dome
2005/08/30 17:41

2005/08/30 17:41

It has been quite some fun to build these two models, and also sense the stability within the dome while building it.

4V 4/8 Dome

I couldn't resist to build also the more complex 4V model, 250 struts to cut, from 63 sticks. So, D was 10cm, or 2D 20cm for the calculator:

r = 32cm, d = 64cm
A = 8.0cm (x 30)
B = 9.4cm (x 30)
C = 9.4cm (x 60)
D = 10.0cm (x 70)
E = 10.4cm (x 30)
F = 9.5cm (x 30)

So, B, C and F are very close, and since cutting so small bamboo so exact is hardly possible for me I made them all the same. The D and E I marked with color to distinct them.

4V 4/8 Dome (Closeup)
Following cuts I made then:

60x C+D
5x D+D
30x A+E
30x B+F

Step by Step

Starting the 4V Model (also parts for other models)
2005/09/10 11:31

63 sticks
2005/09/10 12:13

126 sticks
2005/09/10 12:31

250 sticks: A, B, C, D, E and F
2005/09/10 13:25

The PVC junctions, 85x 6-way and 20x 4-way
2005/09/10 15:23

2005/09/10 15:35

4V 4/8 Dome Model
2005/09/12 12:48

2005/09/12 12:48

2005/09/12 12:49

2005/09/12 12:50

2005/09/12 12:51

Size Comparison with Hand
2005/09/12 12:52

The 4V 4/8 dome came out very well, the 4mm pipe isn't narrow enough for the bamboo thereby the dome isn't as stable, e.g. when moving around. It would be better to have actually 1mm less diameter of the inner diameter of the pipe than the thickness of the sticks. So far, the 4V looks more filigree than the 3V I think, less edgy, obvious due higher subdivision.

2V Geodesic Cuboctahedron Dome

Geodesic Cuboctahedron Dome L2 Model (46cm diameter)

Geodesic Cuboctahedron Dome L2 Model (Closeup)

I made following model again with 4mm thick and 40cm long bamboo, and 6mm/4mm clear PVC pipe as connector. A quick check how to optimize the struts:

Vertices/Connectors: 39
- 15 x 4-way
- 24 x 6-way
Faces: 64 (3-sided)
Edges/Struts:
- A x 24: 0.39018
- B x 24: 0.42291
- C x 30: 0.51764
- D x 12: 0.54120
- E x 12: 0.57735
total 102 struts (5 kinds)
strut variance 47.9%
diameter: 2.000, radius: 1.000
height: 0.943 or 47.15% of diameter

So I optimize:

12 x (A + E) = 1.0
12 x (A + D)
24 x (B + C)
6 x C
total 54 laths

(A+E) = 1.0, therefore
- A = 0.403, B = 0.436, C = 0.534, D = 0.559, E = 0.596
(A_lath+E_lath) = ~20cm (using 27 x 40cm bamboo equal 54 x 20cm bamboo)
- l_hole = 0.75cm, A_lath = 7.5cm, B_lath = 8.3cm, C_lath = 10.6cm, D_lath = 11.1cm, E_lath = 11.9cm

I first calculated A+E (instead of A_lath+E_lath) which made the struts 0.5cm longer A and B, for C, D and E the error was neglectable, but the resulting dome looked strange, until I realized those 0.75cm do really matter at that scale of the model. So I recommend using l_hole even you are doing a model at 10cm scale or so.

I considered the geodesic dome for doing a temporary building or habitat. Using a set of struts, build by wooden roof laths (very cheap and easy to get here in Switzerland), and building a 5-6m diameter dome for myself to live in it. I merely doing the skeleton of the dome (no faces), and put then a cover over it (shape not yet determined).

Following options for a shelter are considered for me, I target diameter from 6m to 8m, for now I focused only on the Icosahedron based domes:

2V 4/8 Icosahedron Dome
2V 4/8 Dome with

l_lath 3m long lath (A+B)
5.62m diameter
35 laths

For my personal taste it's too edgy, and won't really consider it.

3V 4/9 Icosahedron Dome
3V 4/9 Dome with

5.39m diameter
l_lath 2m long lath (B+C)
60 laths

This option looks better, and I have been pondering on it with an additional wall, e.g. lattice wall from the yurt, yet the stability of the wall in this case isn't secured.

3V 5/9 Icosahedron Dome
3V 5/9 Dome with

6.13m diameter
l_lath 2.5m long lath (B+C)
83 laths

Very good head space, yet, the base line isn't straight, and some levelers are required.

4V 4/8 Icosahedron Dome
4V 4/8 Dome with

6.3m diameter, l_lath 1.82m (D+D) bamboo with l_hole 2-3cm
- with total height of 3.1m it would be optionally to make another level, e.g. at 1.8m height for beds
7.10m diameter, l_lath 2.10m (D+D) bamboo with l_hole 2-3cm
- with total height of 3.65m it would be suitable to make another level, at 2m height.
8.05m diameter, l_lath 2.40m (D+D) bamboo with l_hole 2-3cm
- with total height of 4m it would be very obvious to make another level, at 2m height.
125 laths

This I personally consider most nice as it's more smooth and less edgy, yet, the overhead for 250 struts becomes significantly now. In late winter/spring 2007 I started to build a 6.3m diameter 4V 4/8 dome with bamboo struts, consider to read my diary.

Strut Connector

There are flat steel connectors with the form like:

With screws for wood and M10 screw the total cost per strut is about CHF 2.10 - 3.00, which brings the cost quite up, e.g. 4V 4/8 dome 7m diameter costs about CHF 510 or € 330.

Thinking of using bamboo (with variable diameter naturally) is another option, costs apprx. CHF 0.35 per 182cm bamboo (@250 pieces) from a wholesale garden company.

Pipe Connector

In case of round profile struts (such as bamboo) another approach is to use a soft pipe as connector, like LD-PE and squeeze the one end. For variable diameter such as bamboo (or everything naturally grown) the half pipe is more suitable, adapting to variable diameter, using cable binder like this:

LDPE half-pipe with 1 cable binder (1)
2007/01/22 09:02

LDPE half-pipe with 1 cable binder (2)
2007/01/22 09:02

2007/01/22 09:08

The estimated costs are low, for half-pipe only few cents, and one screw per connection (not strut) plus the cable binder also a few cents. This approach with a LDPE pipe is suitable for lightweight tent-like setups, not recommended when the dome is covered with solid cardboard or alike.

Some dome critics describe the problems to insulate the dome because of the many junctions and seams. An architect who worked on domes recommended to me to separate the functions:

static
thermal insulation
water/weather insulation

then each part can be secured individually.

The problem only arises when all functions are targeted to be resolved with one solution, e.g. the static also must provide also water insulation and this is difficult.

Since I focus on "temporary buildings", buildings which can be put up and taken down within a short period of time such as 2-3 hours, this has to be kept in mind.

I haven't yet thought about it in all details, so far two approaches I consider:

water-resistant fabric stripes/leaf-like segments over the dome: cheap fabric, but might such cover hides the beauty of the dome then outside.
wood or cardboard triangle faces to cover entire dome, and use shingles to protects against rain leaking the many strut junction, but this would run against "temporary" building as it wouldn't be such one anymore.

So, the synthetic fabric for the cover seems my option, yet, the beauty of the architecture is covered and vanishes; also a complicated folding or sew pattern is required to have the cover fit closely.

If I use a rectangular blanket, then I require d * π / 2 side length.

This approach provides leaf-like composition to have a half-sphere roof canvas.

Symbols & Formulas:

α = 0 .. 90° c_α = r_α * 2 * π h = r * 2 * π / 4
r_α = cos( α ) * r c_αs = c_α / n_leaves y = h * ( α / 90 )

Edit the diameter d, and amount of segments n_leaves, and the canvas lanes wide w_canvas which is used to patch together a leaf, and then press "calculate".

Leaf composition: interior & rain canvas

Note: Since the calculator for now provides just 4/8 cover, I recommend:

4/9 sphere: reduce it accordingly at the bottom
5/9 sphere: add rectangular lane/stripe, in which you sew a cord which is used to make the bottom of the 1/9 of a 5/9 sphere fit closely (with wrinkels)

If you made experiences yourself with 5/9 sphere with leaf-like cover approach, drop me an email.

In order to sew these leaf-like sphere surface together as rain cover, the water leak is particular to be avoided and so special care of how to sew the seams together:

Options of Seam Sewing

In case of the wigwam a combination of two of the options might be used:

overlay horizontal canvas stripes or lanes to compose a part of a roof leaf or segment
use either one-fold or two-fold to patch the leaves / segments together

Consider to seal the stitching holes from sewing with silicon or good clear tape for canvas (with threads) and preferable use water-resistant sewing thread as well.

4V 4/8 Geodesic Dome with leaf-like segment composed cover
As a test I did a cover for the previously build 4V 4/8 geodesic dome, d = 76 cm, n_leaves = 6.

Step by step of the making of:

Getting the numbers from the 4/8 sphere cover calculator
2006/02/22 09:55

4V 4/8 Geodesic Dome Model
2006/02/22 09:56

Left-over from the yurt cover, PE (180g/m²)
2006/02/22 09:57

Marking the widths
2006/02/22 10:08

Cutting and folding half, leave some extra space for seam (two fold)
2006/02/22 10:10

Leaf/segment template finished with extra width for seam
2006/02/22 10:11

Marking other leaves/segments
2006/02/22 10:12

And so on ...
2006/02/22 10:16

Finished all 6 leaves/segments
2006/02/22 10:29

Using "two fold" to sew leaves/segments together
2006/02/22 10:50

Note that the top ending I didn't sew, it's too narrow
2006/02/22 10:50

Quick test if it roughly fits ...
2006/02/22 10:52

Adding more leaves/segments ...
2006/02/22 11:01

And so on ...
2006/02/22 11:18

Leaf composed 4/8 sphere cover finished
2006/02/22 11:23

4/8 sphere cover (side view)
2006/02/22 11:23

4/8 sphere cover (top view)
2006/02/22 11:24

Interior view of 4V 4/8 geodesic dome with cover (1)
2006/02/22 11:26

Interior view of 4V 4/8 geodesic dome with cover (2)
2006/02/22 11:26

Interior view of 4V 4/8 geodesic dome with cover (3)
2006/02/22 11:26

Interior view of 4V 4/8 geodesic dome with cover (4)
2006/02/22 11:27

As I experienced with this test for the 4V model, the top ending is hard to sew as the "two fold" seam is moderately thick, but overlaying 6 of them is too hard to sew, therefore I did leave it open. For a real life application a (clear) top cover would be build, e.g. a frame along the "top" 5 sided polygon of the 4V dome to hold the top cover.

Maybe I will extend the 4V Model further and test some ideas, let's see.

A special consideration is the door, the triangle usually are too small to climb in (such as in case of a 3V 5/8), so a special strut combination might be use to extend a location to become the door, still triangular but large enough so one can enter the dome.

For now I consider to make the top most strut star covered by transparent plastic, and overlap the other cover, maybe use a four cords to fix the (square) sky cover, like in case of a yurt. Additional windows I will consider, but not yet sure about the weather/rain insulation of such. See my diary for the decision I actually made meanwhile.

Alike a yurt I will put a bright interior cotton cover as first layer, this way the construction is seen from the inside. Additionally putting in a wooden floor composed by laths or larger wooden plates.

Floor Examples

With high ceiling making a 2nd floor for beds is an interesting option, in particular in the winter-time when the heat from the stove rises.

2nd Floor Options in Dome
A few options I quickly drew, keeping the circular shape of the dome for the 2nd floor as well:

"1/4 moon": 2 pieces and 5 columns, best light distribution from the skylight.
"3/4 moon": 1 or 2 pieces, 4 columns
"4/4 moon": 1-4 pieces, 4 columns
"eclipse": 1 or 4 pieces, 4+ columns, the light from the skylight reaches both levels, the 2nd floor and also the base.

Desert Domes: Tips
Worldflower Garden Dome.com , vast site with many variants
PacificDomes.com , wonderful geodesic domes with tent-like setup
Red Sky Shelters , 1V based tents called "Yome"

See also my notes on tipi and yurt.

α = 0 .. 90°	c_α = r_α * 2 * π	h = r * 2 * π / 4
r_α = cos( α ) * r	c_αs = c_α / n_leaves	y = h * ( α / 90 )

Geodesic Dome Notes & Calculator

Table of Content

Changes

Introduction

Origin of the Geodesic Dome

Geodesize: Triangulate & Normalize

Procedure & Evolution of a Subdividing Triangle

The nV Notion

The Ln Notion

The Concated V Notion

The Concated V vs Ln Notion

Normalizing

References

Overview of Variants

Icosahedron-based Geodesic Domes

Octahedron-based Geodesic Domes

Cube-based Geodesic Domes

Cuboctahedron-based Geodesic Domes

Truncated Octahedron-based Geodesic Domes

Rhombicuboctahedron-based Geodesic Domes

Numerical Overview

Amount of Struts vs. Strut Variance

Amount of Struts vs. Strut Types

How to Use the Notes

Strut Options & Notion

Wooden Strut with Flat Connector

Wooden Strut with Pipe Hub

Pipe/Tube based Strut

Bamboo Strut

Bending the Strut-Endings

Detailed Calculation of the Faces or Hub/Strut Angles

The Icosahedron

1V/L1 2/3 Icosahedron Dome

1V 2/3 Icosahedron Dome Calculator

2V/L2 Icosahedron Dome

2V Icosahedron Dome Calculator

3V 4/9 Icosahedron Dome

3V 4/9 Icosahedron Dome Calculator

3V 5/9 Icosahedron Dome

3V 5/9 Icosahedron Dome Calculator

4V Icosahedron Dome

4V Icosahedron Dome Calculator

L3 Icosahedron Dome

L3 Icosahedron Dome Calculator

5V 7/15 Icosahedron Dome

5V 7/15 Icosahedron Dome Calculator

5V 8/15 Icosahedron Dome

5V 8/15 Icosahedron Dome Calculator

6V Icosahedron Dome

6V Icosahedron Dome Calculator

2V.3V Icosahedron Dome

2V.3V Icosahedron Dome Calculator

3V.2V Icosahedron Dome

7V 10/21 Icosahedron Dome

7V 10/21 Icosahedron Dome Calculator

7V 11/21 Icosahedron Dome

7V 11/21 Icosahedron Dome Calculator

8V Icosahedron Dome

8V Icosahedron Dome Calculator

L4 Icosahedron Dome

L4 Icosahedron Dome Calculator

The Octahedron

1V/L1 Octahedron Dome

1V Octahedron Dome Calculator

2V/L2 Octahedron Dome

2V Octahedron Dome Calculator

3V Octahedron Dome

3V Octahedron Dome Calculator

4V Octahedron Dome

4V Octahedron Dome Calculator

L3 Octahedron Dome

L3 Octahedron Dome Calculator

L3 1/4 Octahedron Dome

L3 3/8 Octahedron Dome Calculator

L3 5/8 Octahedron Dome

L3 5/8 Octahedron Dome Calculator

5V Octahedron Dome

5V Octahedron Dome Calculator

6V Octahedron Dome

6V Octahedron Dome Calculator