written by Rene K. Mueller, Copyright (c) 2007, last updated Sat, October 6, 2007
Introduction
After I studied the Geodesic Dome I thought about triangulating also other non-(hemi)spherical forms, e.g. a general Bow Dome as I covered already using Bezier curve to simulate bending of bows.
One of the disadvantages of the dome is that the roof has too litte steep slope in order to have snow slide down, so it would be interesting to have a circular bow dome with a minimum of slope, like a Yurt, yet, triangulated.
Please Note: This is a very preliminary version of the document, and may change dramatically (e.g. such as used notions) or be renamed. In particular I like to optimize the amount of different struts for each version, and later also add an online calculator for each featured option.
Regular Dome
Regular Dome (α = 0°, β = 0°)
Regular Dome
A part of the top area of the dome is where no snow can slide (orange in the illustration), in regions with snow fall this is a disadvantage.
Steep Roof Dome
Steep Roof Dome (α = 25°, β = 0°)
Steep Roof Dome
A steady 25° roof resolves the above mentioned condition.
Dent Roof Dome
Dent Roof Dome (α = 45°, &beta = 0°)
Dent Roof Dome
With a 45° angle from the top, and still remaining vertical start at the bottom, provides an "oriental" shape.
It needs to be said in case of dome, no matter what variant, that the entire surface acts as roof, in other words, all cover requires 100% sealed of rain water.
Stripe Triangulation
The Bezier curve is linearly split into n/2-steps, where n*2 amount of edges of the polygon for the base, that outline is rotated to create a circular space, and triangulated in stripes.
Methods of Stripe Triangulation
There are two ways to stripe triangulate as I focus on (there are many other methods available), keeping the amount of edges constant, or reduce them by half when a certain length is reached:
Method A: Amount of edges kept constant, more narrow triangulation near top
Method B: Amount of edges variable, strut length kept above a minimum
The detail about switching to from 1:1 triangulation to 1:2 when a certain minimum length is reached (aka as "trimming"):
Stripe Triangulation Methods
n = amount of sections (preferable 2n, 3*2n and 5*2n so division by 2 is possible without remainder)
Here an overview of a couple of options, for now I feature only Method B ("trimmed lamella") with 1:2 triangles when it narrows:
Triangulated Bow Dome 0° / 0°
0° / 0° / 6 48 struts (6 kinds)
0° / 0° / 8 76 struts (9 kinds)
0° / 0° / 10 125 struts (11 kinds)
0° / 0° / 12 186 struts (13 kinds)
0° / 0° / 16 308 struts (18 kinds)
0° / 0° / 20 475 struts (22 kinds)
Triangulated Bow Dome 25° / 0°
25° / 0° / 6 48 struts (6 kinds)
25° / 0° / 8 76 struts (9 kinds)
25° / 0° / 10 125 struts (11 kinds)
25° / 0° / 12 186 struts (13 kinds)
25° / 0° / 16 308 struts (18 kinds)
25° / 0° / 20 475 struts (21 kinds)
Triangulated Bow Dome 45° / 0°
45° / 0° / 6 48 struts (6 kinds)
45° / 0° / 8 76 struts (9 kinds)
45° / 0° / 10 125 struts (11 kinds)
45° / 0° / 12 168 struts (13 kinds)
45° / 0° / 16 308 struts (18 kinds)
45° / 0° / 20 475 struts (22 kinds)
T. Bow Dome 0/0/6
Triangulated Bow Dome 0°/0°/6 (front view)
Triangulated Bow Dome 0°/0°/6 (bird view)
Triangulated Bow Dome 0°/0°/6 (top view)
vertices/connectors: 19
6 x 4-way
6 x 5-way
7 x 6-way
Triangulated Bow Dome 0°/0°/6 Construction Map
edges/struts & bending angles (αstrut):
A x 6: 0.52593 (15.25°)
B x 6: 0.54079 (15.69°)
C x 12: 0.60464 (17.60°)
D x 12: 0.72572 (21.28°)
E x 6: 0.87407 (25.91°)
F x 6: 1.00000 (30.00°)
total 48 struts (6 kinds)1)
strut variance 90.2%
faces: 30 (3-sided)
A-B-B x 6 (58.19°, 60.91°, 60.91°)
A-C-C x 6 (51.56°, 64.22°, 64.22°)
C-C-E x 6 (43.71°, 43.71°, 92.58°)
D-D-E x 6 (52.97°, 52.97°, 74.06°)
D-D-F x 6 (46.45°, 46.45°, 87.10°)
5 kinds of faces2)
diameter: 2.040, radius: 1.020
height: 1.000 or 49.01% 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
T. Bow Dome 0/0/8
Triangulated Bow Dome 0°/0°/8 (front view)
Triangulated Bow Dome 0°/0°/8 (bird view)
Triangulated Bow Dome 0°/0°/8 (top view)
vertices/connectors: 29
9 x 4-way
4 x 5-way
16 x 6-way
Triangulated Bow Dome 0°/0°/8 Construction Map
edges/struts & bending angles (αstrut):
A x 4: 0.37534 (10.82°)
B x 4: 0.41564 (11.99°)
C x 16: 0.49328 (14.28°)
D x 8: 0.55489 (16.11°)
E x 16: 0.56040 (16.27°)
F x 8: 0.56102 (16.29°)
G x 4: 0.57894 (16.83°)
H x 8: 0.71036 (20.80°)
I x 8: 0.76537 (22.50°)
total 76 struts (9 kinds)1)
strut variance 103.9%
faces: 48 (3-sided)
A-D-F x 8 (39.30°, 69.47°, 71.23°)
B-B-G x 4 (45.86°, 45.86°, 88.29°)
C-C-D x 8 (55.78°, 55.78°, 68.45°)
C-C-H x 8 (43.94°, 43.94°, 92.12°)
E-E-H x 8 (50.67°, 50.67°, 78.67°)
E-E-I x 8 (46.93°, 46.93°, 86.14°)
F-F-G x 4 (58.94°, 58.94°, 62.12°)
7 kinds of faces2)
diameter: 2.051, radius: 1.025
height: 1.000 or 48.77% 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
T. Bow Dome 0/0/10
Triangulated Bow Dome 0°/0°/10 (front view)
Triangulated Bow Dome 0°/0°/10 (bird view)
Triangulated Bow Dome 0°/0°/10 (top view)
vertices/connectors: 46
10 x 4-way
6 x 5-way
30 x 6-way
Triangulated Bow Dome 0°/0°/10 Construction Map
edges/struts & bending angles (αstrut):
A x 5: 0.30701 (8.83°)
B x 5: 0.33760 (9.72°)
C x 20: 0.37010 (10.66°)
D x 10: 0.37774 (10.89°)
E x 5: 0.39311 (11.34°)
F x 20: 0.41337 (11.93°)
G x 10: 0.41512 (11.98°)
H x 20: 0.45533 (13.16°)
I x 10: 0.50728 (14.69°)
J x 10: 0.58936 (17.14°)
K x 10: 0.61803 (18.00°)
total 125 struts (11 kinds)1)
strut variance 101.3%
faces: 80 (3-sided)
A-D-G x 10 (45.26°, 60.91°, 73.83°)
B-B-E x 5 (54.39°, 54.39°, 71.21°)
C-C-D x 10 (59.32°, 59.32°, 61.36°)
C-C-I x 10 (46.74°, 46.74°, 86.53°)
E-G-G x 5 (56.52°, 61.74°, 61.74°)
F-F-I x 10 (52.15°, 52.15°, 75.70°)
F-F-J x 10 (44.53°, 44.53°, 90.94°)
H-H-J x 10 (49.66°, 49.66°, 80.67°)
H-H-K x 10 (47.26°, 47.26°, 85.48°)
9 kinds of faces2)
diameter: 2.047, radius: 1.023
height: 1.000 or 48.86% 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
T. Bow Dome 0/0/12
Triangulated Bow Dome 0°/0°/12 (front view)
Triangulated Bow Dome 0°/0°/12 (bird view)
Triangulated Bow Dome 0°/0°/12 (top view)
vertices/connectors: 67
12 x 4-way
6 x 5-way
49 x 6-way
Triangulated Bow Dome 0°/0°/12 Construction Map
edges/struts & bending angles (αstrut):
A x 6: 0.26086 (7.49°)
B x 12: 0.27224 (7.82°)
C x 6: 0.28241 (8.12°)
D x 6: 0.28426 (8.17°)
E x 24: 0.29638 (8.52°)
F x 24: 0.32410 (9.33°)
G x 12: 0.32840 (9.45°)
H x 24: 0.35452 (10.21°)
I x 12: 0.37529 (10.82°)
J x 24: 0.38307 (11.04°)
K x 12: 0.45245 (13.07°)
L x 12: 0.50086 (14.50°)
M x 12: 0.51764 (15.00°)
total 186 struts (13 kinds)1)
strut variance 98.4%
faces: 120 (3-sided)
A-B-G x 12 (50.44°, 53.54°, 76.02°)
B-E-E x 12 (54.67°, 62.67°, 62.67°)
C-D-D x 6 (59.56°, 60.22°, 60.22°)
C-G-G x 6 (50.93°, 64.53°, 64.53°)
E-E-I x 12 (50.72°, 50.72°, 78.56°)
F-F-I x 12 (54.62°, 54.62°, 70.76°)
F-F-K x 12 (45.73°, 45.73°, 88.55°)
H-H-K x 12 (50.34°, 50.34°, 79.32°)
H-H-L x 12 (45.05°, 45.05°, 89.90°)
J-J-L x 12 (49.18°, 49.18°, 81.65°)
J-J-M x 12 (47.50°, 47.50°, 84.99°)
11 kinds of faces2)
diameter: 2.051, radius: 1.025
height: 1.000 or 48.77% 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
T. Bow Dome 0/0/16
Triangulated Bow Dome 0°/0°/16 (front view)
Triangulated Bow Dome 0°/0°/16 (bird view)
Triangulated Bow Dome 0°/0°/16 (top view)
vertices/connectors: 109
17 x 4-way
8 x 5-way
80 x 6-way
4 x 7-way
Triangulated Bow Dome 0°/0°/16 Construction Map
edges/struts & bending angles (αstrut):
A x 8: 0.19129 (5.49°)
B x 4: 0.20138 (5.78°)
C x 4: 0.21602 (6.20°)
D x 32: 0.22540 (6.47°)
E x 16: 0.22634 (6.50°)
F x 32: 0.24103 (6.92°)
G x 32: 0.25810 (7.41°)
H x 16: 0.26971 (7.75°)
I x 32: 0.27489 (7.90°)
J x 16: 0.28288 (8.13°)
K x 32: 0.29049 (8.35°)
L x 8: 0.30359 (8.73°)
M x 4: 0.30439 (8.75°)
N x 8: 0.31332 (9.01°)
O x 16: 0.32845 (9.45°)
P x 16: 0.36214 (10.43°)
Q x 16: 0.38302 (11.04°)
R x 16: 0.39018 (11.25°)
total 308 struts (18 kinds)1)
strut variance 104.0%
faces: 200 (3-sided)
A-E-H x 16 (44.31°, 55.72°, 79.98°)
B-L-N x 8 (38.07°, 68.36°, 73.58°)
C-C-M x 4 (45.20°, 45.20°, 89.60°)
D-D-E x 16 (59.87°, 59.87°, 60.26°)
D-D-J x 16 (51.13°, 51.13°, 77.74°)
F-F-J x 16 (54.06°, 54.06°, 71.88°)
F-F-O x 16 (47.04°, 47.04°, 85.93°)
G-G-O x 16 (50.48°, 50.48°, 79.05°)
G-G-P x 16 (45.45°, 45.45°, 89.09°)
H-H-N x 8 (54.49°, 54.49°, 71.02°)
I-I-P x 16 (48.81°, 48.81°, 82.39°)
I-I-Q x 16 (45.84°, 45.84°, 88.31°)
K-K-Q x 16 (48.76°, 48.76°, 82.48°)
K-K-R x 16 (47.81°, 47.81°, 84.38°)
L-L-M x 4 (59.91°, 59.91°, 60.17°)
15 kinds of faces2)
diameter: 2.051, radius: 1.025
height: 1.000 or 48.77% 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
T. Bow Dome 0/0/20
Triangulated Bow Dome 0°/0°/20 (front view)
Triangulated Bow Dome 0°/0°/20 (bird view)
Triangulated Bow Dome 0°/0°/20 (top view)
vertices/connectors: 166
20 x 4-way
16 x 5-way
120 x 6-way
10 x 7-way
Triangulated Bow Dome 0°/0°/20 Construction Map
edges/struts & bending angles (αstrut):
A x 10: 0.15141 (4.34°)
B x 5: 0.16428 (4.71°)
C x 5: 0.17420 (5.00°)
D x 40: 0.18177 (5.21°)
E x 20: 0.19123 (5.49°)
F x 40: 0.19178 (5.50°)
G x 20: 0.20066 (5.76°)
H x 40: 0.20264 (5.82°)
I x 5: 0.20431 (5.86°)
J x 10: 0.20667 (5.93°)
K x 40: 0.21355 (6.13°)
L x 10: 0.22179 (6.37°)
M x 40: 0.22404 (6.43°)
N x 20: 0.22683 (6.51°)
O x 20: 0.22733 (6.53°)
P x 40: 0.23383 (6.71°)
Q x 20: 0.25680 (7.38°)
R x 20: 0.28077 (8.07°)
S x 10: 0.29703 (8.54°)
T x 20: 0.29835 (8.58°)
U x 20: 0.30918 (8.89°)
V x 20: 0.31287 (9.00°)
total 475 struts (22 kinds)1)
strut variance 106.7%
faces: 310 (3-sided)
A-E-O x 20 (41.30°, 56.46°, 82.24°)
B-J-L x 10 (44.92°, 62.67°, 72.41°)
C-C-I x 5 (54.10°, 54.10°, 71.80°)
D-D-E x 20 (58.27°, 58.27°, 63.45°)
D-D-N x 20 (51.41°, 51.41°, 77.18°)
F-F-N x 20 (53.75°, 53.75°, 72.49°)
F-F-Q x 20 (47.98°, 47.98°, 84.05°)
G-G-J x 10 (59.01°, 59.01°, 61.99°)
G-G-S x 10 (42.28°, 42.28°, 95.45°)
H-H-Q x 20 (50.67°, 50.67°, 78.66°)
H-H-R x 20 (46.13°, 46.13°, 87.73°)
I-L-L x 5 (54.85°, 62.58°, 62.58°)
K-K-R x 20 (48.88°, 48.88°, 82.24°)
K-K-T x 20 (45.67°, 45.67°, 88.67°)
M-M-T x 20 (48.24°, 48.24°, 83.53°)
M-M-U x 20 (46.36°, 46.36°, 87.29°)
O-O-S x 10 (49.21°, 49.21°, 81.59°)
P-P-U x 20 (48.60°, 48.60°, 82.79°)
P-P-V x 20 (48.00°, 48.00°, 84.00°)
19 kinds of faces2)
diameter: 2.051, radius: 1.025
height: 1.000 or 48.77% 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
T. Bow Dome 25/0/6
Triangulated Bow Dome 25°/0°/6 (front view)
Triangulated Bow Dome 25°/0°/6 (bird view)
Triangulated Bow Dome 25°/0°/6 (top view)
vertices/connectors: 19
6 x 4-way
6 x 5-way
7 x 6-way
Triangulated Bow Dome 25°/0°/6 Construction Map
edges/struts & bending angles (αstrut):
A x 6: 0.50095 (14.51°)
B x 6: 0.55487 (16.11°)
C x 12: 0.57521 (16.71°)
D x 12: 0.68595 (20.06°)
E x 6: 0.86159 (25.52°)
F x 6: 1.00000 (30.00°)
total 48 struts (6 kinds)1)
strut variance 99.6%
faces: 30 (3-sided)
A-B-B x 6 (53.67°, 63.16°, 63.16°)
A-C-C x 6 (51.63°, 64.18°, 64.18°)
C-C-E x 6 (41.50°, 41.50°, 97.00°)
D-D-E x 6 (51.09°, 51.09°, 77.82°)
D-D-F x 6 (43.20°, 43.20°, 93.60°)
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
T. Bow Dome 25/0/8
Triangulated Bow Dome 25°/0°/8 (front view)
Triangulated Bow Dome 25°/0°/8 (bird view)
Triangulated Bow Dome 25°/0°/8 (top view)
vertices/connectors: 29
9 x 4-way
4 x 5-way
16 x 6-way
Triangulated Bow Dome 25°/0°/8 Construction Map
edges/struts & bending angles (αstrut):
A x 4: 0.37130 (10.70°)
B x 4: 0.42511 (12.27°)
C x 16: 0.45939 (13.28°)
D x 16: 0.53491 (15.51°)
E x 8: 0.53876 (15.63°)
F x 8: 0.54488 (15.81°)
G x 4: 0.54542 (15.83°)
H x 8: 0.70431 (20.62°)
I x 8: 0.76537 (22.50°)
total 76 struts (9 kinds)1)
strut variance 106.1%
faces: 48 (3-sided)
A-E-F x 8 (40.07°, 69.08°, 70.85°)
B-B-G x 4 (50.10°, 50.10°, 79.81°)
C-C-E x 8 (54.10°, 54.10°, 71.81°)
C-C-H x 8 (39.96°, 39.96°, 100.09°)
D-D-H x 8 (48.83°, 48.83°, 82.35°)
D-D-I x 8 (44.32°, 44.32°, 91.36°)
F-F-G x 4 (59.97°, 59.97°, 60.06°)
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
T. Bow Dome 25/0/10
Triangulated Bow Dome 25°/0°/10 (front view)
Triangulated Bow Dome 25°/0°/10 (bird view)
Triangulated Bow Dome 25°/0°/10 (top view)
vertices/connectors: 46
10 x 4-way
6 x 5-way
30 x 6-way
Triangulated Bow Dome 25°/0°/10 Construction Map
edges/struts & bending angles (αstrut):
A x 5: 0.31008 (8.92°)
B x 5: 0.34427 (9.91°)
C x 20: 0.35154 (10.12°)
D x 10: 0.36274 (10.45°)
E x 5: 0.36774 (10.60°)
F x 20: 0.38385 (11.07°)
G x 10: 0.40777 (11.76°)
H x 20: 0.43776 (12.64°)
I x 10: 0.49728 (14.40°)
J x 10: 0.58602 (17.04°)
K x 10: 0.61803 (18.00°)
total 125 struts (11 kinds)1)
strut variance 99.3%
faces: 80 (3-sided)
A-D-G x 10 (47.02°, 58.83°, 74.16°)
B-B-E x 5 (57.73°, 57.73°, 64.55°)
C-C-D x 10 (58.94°, 58.94°, 62.12°)
C-C-I x 10 (44.98°, 44.98°, 90.05°)
E-G-G x 5 (53.59°, 63.20°, 63.20°)
F-F-I x 10 (49.63°, 49.63°, 80.74°)
F-F-J x 10 (40.25°, 40.25°, 99.50°)
H-H-J x 10 (47.99°, 47.99°, 84.02°)
H-H-K x 10 (45.11°, 45.11°, 89.79°)
9 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
T. Bow Dome 25/0/12
Triangulated Bow Dome 25°/0°/12 (front view)
Triangulated Bow Dome 25°/0°/12 (bird view)
Triangulated Bow Dome 25°/0°/12 (top view)
vertices/connectors: 67
12 x 4-way
6 x 5-way
49 x 6-way
Triangulated Bow Dome 25°/0°/12 Construction Map
edges/struts & bending angles (αstrut):
A x 12: 0.25931 (7.45°)
B x 6: 0.26290 (7.55°)
C x 6: 0.26577 (7.64°)
D x 24: 0.28725 (8.26°)
E x 6: 0.28917 (8.31°)
F x 24: 0.30315 (8.72°)
G x 12: 0.32546 (9.37°)
H x 24: 0.33007 (9.50°)
I x 12: 0.36438 (10.50°)
J x 24: 0.37029 (10.67°)
K x 12: 0.44599 (12.89°)
L x 12: 0.49884 (14.44°)
M x 12: 0.51764 (15.00°)
total 186 struts (13 kinds)1)
strut variance 99.6%
faces: 120 (3-sided)
A-C-G x 12 (50.80°, 52.60°, 76.60°)
A-D-D x 12 (53.65°, 63.17°, 63.17°)
B-E-E x 6 (54.07°, 62.97°, 62.97°)
B-G-G x 6 (47.64°, 66.18°, 66.18°)
D-D-I x 12 (50.64°, 50.64°, 78.72°)
F-F-I x 12 (53.05°, 53.05°, 73.90°)
F-F-K x 12 (42.63°, 42.63°, 94.74°)
H-H-K x 12 (47.50°, 47.50°, 84.99°)
H-H-L x 12 (40.93°, 40.93°, 98.14°)
J-J-L x 12 (47.66°, 47.66°, 84.68°)
J-J-M x 12 (45.66°, 45.66°, 88.68°)
11 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
T. Bow Dome 25/0/16
Triangulated Bow Dome 25°/0°/16 (front view)
Triangulated Bow Dome 25°/0°/16 (bird view)
Triangulated Bow Dome 25°/0°/16 (top view)
vertices/connectors: 109
17 x 4-way
8 x 5-way
80 x 6-way
4 x 7-way
Triangulated Bow Dome 25°/0°/16 Construction Map
edges/struts & bending angles (αstrut):
A x 8: 0.19247 (5.52°)
B x 4: 0.20614 (5.92°)
C x 16: 0.21670 (6.22°)
D x 32: 0.21721 (6.23°)
E x 4: 0.21897 (6.29°)
F x 32: 0.22612 (6.49°)
G x 32: 0.23959 (6.88°)
H x 32: 0.25817 (7.42°)
I x 16: 0.26392 (7.58°)
J x 16: 0.27466 (7.89°)
K x 4: 0.28157 (8.09°)
L x 32: 0.28288 (8.13°)
M x 8: 0.29518 (8.49°)
N x 8: 0.29576 (8.50°)
O x 16: 0.32267 (9.28°)
P x 16: 0.35905 (10.34°)
Q x 16: 0.38212 (11.01°)
R x 16: 0.39018 (11.25°)
total 308 struts (18 kinds)1)
strut variance 102.7%
faces: 200 (3-sided)
A-C-I x 16 (45.93°, 53.99°, 80.08°)
B-M-N x 8 (40.82°, 69.43°, 69.75°)
C-D-D x 16 (59.85°, 60.08°, 60.08°)
D-D-J x 16 (50.78°, 50.78°, 78.45°)
E-E-K x 4 (49.99°, 49.99°, 80.02°)
F-F-J x 16 (52.59°, 52.59°, 74.81°)
F-F-O x 16 (44.47°, 44.47°, 91.06°)
G-G-O x 16 (47.67°, 47.67°, 84.66°)
G-G-P x 16 (41.48°, 41.48°, 97.04°)
H-H-P x 16 (45.96°, 45.96°, 88.09°)
H-H-Q x 16 (42.27°, 42.27°, 95.45°)
I-I-M x 8 (55.99°, 55.99°, 68.02°)
K-N-N x 4 (56.85°, 61.58°, 61.58°)
L-L-Q x 16 (47.52°, 47.52°, 84.96°)
L-L-R x 16 (46.40°, 46.40°, 87.20°)
15 kinds of faces2)
diameter: 2.001, radius: 1.001
height: 1.000 or 49.97% 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
T. Bow Dome 25/0/20
Triangulated Bow Dome 25°/0°/20 (front view)
Triangulated Bow Dome 25°/0°/20 (bird view)
Triangulated Bow Dome 25°/0°/20 (top view)
vertices/connectors: 166
20 x 4-way
16 x 5-way
120 x 6-way
10 x 7-way
Triangulated Bow Dome 25°/0°/20 Construction Map
edges/struts & bending angles (αstrut):
A x 10: 0.15070 (4.32°)
B x 5: 0.16810 (4.82°)
C x 40: 0.17459 (5.01°)
D x 5: 0.17617 (5.05°)
E x 40: 0.18028 (5.17°)
F x 20: 0.18363 (5.27°)
G x 45: 0.18826 (5.40°)
H x 10: 0.19333 (5.55°)
I x 20: 0.19849 (5.70°)
J x 40: 0.19878 (5.70°)
K x 40: 0.21213 (6.09°)
L x 10: 0.21770 (6.25°)
M x 20: 0.22024 (6.32°)
N x 20: 0.22113 (6.35°)
O x 40: 0.22879 (6.57°)
P x 20: 0.25174 (7.23°)
Q x 20: 0.27745 (7.97°)
R x 10: 0.28171 (8.10°)
S x 20: 0.29666 (8.53°)
T x 20: 0.30870 (8.88°)
U x 20: 0.31287 (9.00°)
total 475 struts (21 kinds)1)
strut variance 107.6%
faces: 310 (3-sided)
A-F-N x 20 (42.47°, 55.35°, 82.17°)
B-H-L x 10 (47.83°, 58.46°, 73.71°)
C-C-F x 20 (58.28°, 58.28°, 63.44°)
C-C-M x 20 (50.91°, 50.91°, 78.19°)
D-D-G x 5 (57.70°, 57.70°, 64.60°)
E-E-M x 20 (52.36°, 52.36°, 75.27°)
E-E-P x 20 (45.73°, 45.73°, 88.53°)
G-G-P x 20 (48.06°, 48.06°, 83.88°)
G-G-Q x 20 (42.56°, 42.56°, 94.88°)
G-L-L x 5 (51.25°, 64.38°, 64.38°)
H-I-I x 10 (58.27°, 60.86°, 60.86°)
I-I-R x 10 (44.80°, 44.80°, 90.40°)
J-J-Q x 20 (45.76°, 45.76°, 88.48°)
J-J-S x 20 (41.74°, 41.74°, 96.53°)
K-K-S x 20 (45.62°, 45.62°, 88.76°)
K-K-T x 20 (43.30°, 43.30°, 93.39°)
N-N-R x 10 (50.43°, 50.43°, 79.14°)
O-O-T x 20 (47.58°, 47.58°, 84.85°)
O-O-U x 20 (46.86°, 46.86°, 86.28°)
19 kinds of faces2)
diameter: 2.001, radius: 1.001
height: 1.000 or 49.96% 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
T. Bow Dome 45/0/6
Triangulated Bow Dome 45°/0°/6 (front view)
Triangulated Bow Dome 45°/0°/6 (bird view)
Triangulated Bow Dome 45°/0°/6 (top view)
vertices/connectors: 19
6 x 4-way
6 x 5-way
7 x 6-way
Triangulated Bow Dome 45°/0°/6 Construction Map
edges/struts & bending angles (αstrut):
A x 6: 0.44785 (12.94°)
B x 6: 0.54722 (15.88°)
C x 12: 0.56087 (16.29°)
D x 12: 0.66128 (19.31°)
E x 6: 0.83504 (24.68°)
F x 6: 1.00000 (30.00°)
total 48 struts (6 kinds)1)
strut variance 123.3%
faces: 30 (3-sided)
A-B-B x 6 (48.32°, 65.84°, 65.84°)
A-C-C x 6 (47.07°, 66.47°, 66.47°)
C-C-E x 6 (41.90°, 41.90°, 96.20°)
D-D-E x 6 (50.85°, 50.85°, 78.30°)
D-D-F x 6 (40.88°, 40.88°, 98.24°)
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
T. Bow Dome 45/0/8
Triangulated Bow Dome 45°/0°/8 (front view)
Triangulated Bow Dome 45°/0°/8 (bird view)
Triangulated Bow Dome 45°/0°/8 (top view)
vertices/connectors: 29
9 x 4-way
4 x 5-way
16 x 6-way
Triangulated Bow Dome 45°/0°/8 Construction Map
edges/struts & bending angles (αstrut):
A x 4: 0.37211 (10.72°)
B x 4: 0.41871 (12.08°)
C x 16: 0.44394 (12.82°)
D x 4: 0.47413 (13.71°)
E x 8: 0.50447 (14.61°)
F x 8: 0.51760 (15.00°)
G x 16: 0.51882 (15.04°)
H x 8: 0.69145 (20.23°)
I x 8: 0.76537 (22.50°)
total 76 struts (9 kinds)1)
strut variance 105.7%
faces: 48 (3-sided)
A-E-F x 8 (42.67°, 66.78°, 70.54°)
B-B-D x 4 (55.52°, 55.52°, 68.97°)
C-C-E x 8 (55.37°, 55.37°, 69.26°)
C-C-H x 8 (38.84°, 38.84°, 102.32°)
D-F-F x 4 (54.51°, 62.74°, 62.74°)
G-G-H x 8 (48.21°, 48.21°, 83.59°)
G-G-I x 8 (42.47°, 42.47°, 95.07°)
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
T. Bow Dome 45/0/10
Triangulated Bow Dome 45°/0°/10 (front view)
Triangulated Bow Dome 45°/0°/10 (bird view)
Triangulated Bow Dome 45°/0°/10 (top view)
vertices/connectors: 46
10 x 4-way
6 x 5-way
30 x 6-way
Triangulated Bow Dome 45°/0°/10 Construction Map
edges/struts & bending angles (αstrut):
A x 5: 0.30900 (8.89°)
B x 5: 0.31381 (9.03°)
C x 10: 0.33084 (9.52°)
D x 5: 0.33921 (9.76°)
E x 20: 0.34292 (9.87°)
F x 20: 0.36948 (10.65°)
G x 10: 0.38738 (11.17°)
H x 20: 0.42655 (12.31°)
I x 10: 0.47601 (13.77°)
J x 10: 0.57893 (16.83°)
K x 10: 0.61803 (18.00°)
total 125 struts (11 kinds)1)
strut variance 100.0%
faces: 80 (3-sided)
A-C-G x 10 (50.21°, 55.35°, 74.44°)
B-D-D x 5 (55.10°, 62.45°, 62.45°)
B-G-G x 5 (47.78°, 66.11°, 66.11°)
C-E-E x 10 (57.68°, 61.16°, 61.16°)
E-E-I x 10 (46.05°, 46.05°, 87.91°)
F-F-I x 10 (49.90°, 49.90°, 80.20°)
F-F-J x 10 (38.43°, 38.43°, 103.14°)
H-H-J x 10 (47.26°, 47.26°, 85.48°)
H-H-K x 10 (43.57°, 43.57°, 92.85°)
9 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
T. Bow Dome 45/0/12
Triangulated Bow Dome 45°/0°/12 (front view)
Triangulated Bow Dome 45°/0°/12 (bird view)
Triangulated Bow Dome 45°/0°/12 (top view)
vertices/connectors: 61
12 x 4-way
12 x 5-way
31 x 6-way
6 x 7-way
Triangulated Bow Dome 45°/0°/12 Construction Map
edges/struts & bending angles (αstrut):
A x 6: 0.22141 (6.36°)
B x 6: 0.24278 (6.97°)
C x 6: 0.28516 (8.20°)
D x 24: 0.29408 (8.46°)
E x 12: 0.30985 (8.91°)
F x 24: 0.31748 (9.13°)
G x 12: 0.34119 (9.82°)
H x 24: 0.36205 (10.43°)
I x 12: 0.37154 (10.71°)
J x 12: 0.43225 (12.48°)
K x 6: 0.44785 (12.94°)
L x 12: 0.49455 (14.32°)
M x 12: 0.51764 (15.00°)
total 168 struts (13 kinds)1)
strut variance 133.8%
faces: 108 (3-sided)
A-C-C x 6 (45.68°, 67.16°, 67.16°)
A-E-E x 6 (41.86°, 69.07°, 69.07°)
B-G-I x 12 (39.55°, 63.48°, 76.97°)
D-D-G x 12 (54.54°, 54.54°, 70.91°)
D-D-J x 12 (42.70°, 42.70°, 94.61°)
E-E-K x 6 (43.73°, 43.73°, 92.55°)
F-F-J x 12 (47.09°, 47.09°, 85.81°)
F-F-L x 12 (38.85°, 38.85°, 102.29°)
H-H-L x 12 (46.92°, 46.92°, 86.16°)
H-H-M x 12 (44.36°, 44.36°, 91.27°)
I-I-K x 6 (52.93°, 52.93°, 74.15°)
11 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
T. Bow Dome 45/0/16
Triangulated Bow Dome 45°/0°/16 (front view)
Triangulated Bow Dome 45°/0°/16 (bird view)
Triangulated Bow Dome 45°/0°/16 (top view)
vertices/connectors: 109
17 x 4-way
8 x 5-way
80 x 6-way
4 x 7-way
Triangulated Bow Dome 45°/0°/16 Construction Map
edges/struts & bending angles (αstrut):
A x 8: 0.19207 (5.51°)
B x 16: 0.19621 (5.63°)
C x 4: 0.20325 (5.83°)
D x 32: 0.21249 (6.10°)
E x 4: 0.21633 (6.21°)
F x 32: 0.21974 (6.31°)
G x 32: 0.23090 (6.63°)
H x 4: 0.23306 (6.69°)
I x 32: 0.24888 (7.15°)
J x 16: 0.25012 (7.18°)
K x 8: 0.25660 (7.37°)
L x 16: 0.25718 (7.39°)
M x 8: 0.27143 (7.80°)
N x 32: 0.27792 (7.99°)
O x 16: 0.31038 (8.93°)
P x 16: 0.35250 (10.15°)
Q x 16: 0.38021 (10.96°)
R x 16: 0.39018 (11.25°)
total 308 struts (18 kinds)1)
strut variance 103.1%
faces: 200 (3-sided)
A-B-J x 16 (49.19°, 50.62°, 80.19°)
B-D-D x 16 (54.99°, 62.51°, 62.51°)
C-K-M x 8 (45.16°, 63.56°, 71.28°)
D-D-L x 16 (52.76°, 52.76°, 74.48°)
E-E-H x 4 (57.40°, 57.40°, 65.21°)
F-F-L x 16 (54.17°, 54.17°, 71.65°)
F-F-O x 16 (45.06°, 45.06°, 89.89°)
G-G-O x 16 (47.77°, 47.77°, 84.47°)
G-G-P x 16 (40.24°, 40.24°, 99.52°)
H-M-M x 4 (50.86°, 64.57°, 64.57°)
I-I-P x 16 (44.92°, 44.92°, 90.16°)
I-I-Q x 16 (40.20°, 40.20°, 99.59°)
J-J-K x 8 (59.14°, 59.14°, 61.73°)
N-N-Q x 16 (46.84°, 46.84°, 86.32°)
N-N-R x 16 (45.41°, 45.41°, 89.18°)
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
T. Bow Dome 45/0/20
Triangulated Bow Dome 45°/0°/20 (front view)
Triangulated Bow Dome 45°/0°/20 (bird view)
Triangulated Bow Dome 45°/0°/20 (top view)
vertices/connectors: 166
20 x 4-way
16 x 5-way
120 x 6-way
10 x 7-way
Triangulated Bow Dome 45°/0°/20 Construction Map
edges/struts & bending angles (αstrut):
A x 10: 0.15089 (4.33°)
B x 5: 0.15413 (4.42°)
C x 10: 0.16498 (4.73°)
D x 5: 0.16542 (4.74°)
E x 20: 0.16748 (4.80°)
F x 40: 0.17073 (4.90°)
G x 5: 0.17432 (5.00°)
H x 40: 0.17536 (5.03°)
I x 40: 0.18186 (5.22°)
J x 20: 0.18852 (5.41°)
K x 40: 0.19129 (5.49°)
L x 10: 0.20182 (5.79°)
M x 40: 0.20522 (5.89°)
N x 20: 0.20622 (5.92°)
O x 20: 0.20951 (6.01°)
P x 40: 0.22549 (6.47°)
Q x 20: 0.24097 (6.92°)
R x 10: 0.24915 (7.16°)
S x 20: 0.27038 (7.77°)
T x 20: 0.29308 (8.43°)
U x 20: 0.30769 (8.85°)
V x 20: 0.31287 (9.00°)
total 475 struts (22 kinds)1)
strut variance 107.4%
faces: 310 (3-sided)
A-E-O x 20 (45.52°, 52.37°, 82.11°)
B-G-G x 5 (52.47°, 63.77°, 63.77°)
B-L-L x 5 (44.89°, 67.55°, 67.55°)
C-D-L x 10 (52.26°, 52.44°, 75.29°)
C-J-J x 10 (51.91°, 64.05°, 64.05°)
E-F-F x 20 (58.76°, 60.62°, 60.62°)
F-F-N x 20 (52.84°, 52.84°, 74.31°)
H-H-N x 20 (54.00°, 54.00°, 72.00°)
H-H-Q x 20 (46.61°, 46.61°, 86.79°)
I-I-Q x 20 (48.51°, 48.51°, 82.97°)
I-I-S x 20 (41.99°, 41.99°, 96.02°)
J-J-R x 10 (48.62°, 48.62°, 82.75°)
K-K-S x 20 (45.03°, 45.03°, 89.94°)
K-K-T x 20 (40.00°, 40.00°, 100.01°)
M-M-T x 20 (44.42°, 44.42°, 91.15°)
M-M-U x 20 (41.43°, 41.43°, 97.14°)
O-O-R x 10 (53.51°, 53.51°, 72.99°)
P-P-U x 20 (46.98°, 46.98°, 86.04°)
P-P-V x 20 (46.07°, 46.07°, 87.86°)
19 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
For truly bow based approach, without triangulation, see Bow Dome which also includes canvas calculator which could be used to cover the triangulated approach.
, useful writeup and overview
Triangulated Bow Dome 0°/0°/6 Construction Map
