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# Geodesic Dome Notes & Calculator

written by Rene K. Mueller, Copyright (c) 2005, 2006, 2007, last updated Tue, January 29, 2019

### 7V Octahedron Dome

 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 (αstrut):
• 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)
• 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

#### 7V Octahedron Dome Calculator

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

d = , lhole =
(Edit numbers & hit TAB to recalculate)

• Alath = x 16,
• Blath = x 24,
• Clath = x 16,
• Dlath = x 12,
• Elath = x 24,
• Flath = x 24,
• Glath = x 16,
• Hlath = x 24,
• Ilath = x 24,
• Jlath = x 24,
• Klath = x 8,
• Llath = x 24,
• Mlath = x 12,
• Nlath = x 24,
• Olath = x 24,
• Plath = x 12,
• h =

### 8V Octahedron Dome

 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 (αstrut):
• 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)
• 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

#### 8V Octahedron Dome Calculator

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

d = , lhole =
(Edit numbers & hit TAB to recalculate)

• Alath = x 16,
• Blath = x 24,
• Clath = x 16,
• Dlath = x 24,
• Elath = x 12,
• Flath = x 24,
• Glath = x 16,
• Hlath = x 24,
• Ilath = x 24,
• Jlath = x 24,
• Klath = x 24,
• Llath = x 16,
• Mlath = x 24,
• Nlath = x 24,
• Olath = x 12,
• Plath = x 24,
• Qlath = x 12,
• Rlath = x 24,
• Slath = x 24,
• Tlath = x 12,
• h =

### L4 Octahedron Dome

 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 (αstrut):
• 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)
• 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

#### L4 Octahedron Dome Calculator

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

d = , lhole =
(Edit numbers & hit TAB to recalculate)

• Alath = x 64,
• Blath = x 24,
• Clath = x 24,
• Dlath = x 48,
• Elath = x 24,
• Flath = x 24,
• Glath = x 48,
• Hlath = x 24,
• Ilath = x 24,
• Jlath = x 24,
• Klath = x 12,
• Llath = x 12,
• Mlath = x 24,
• Nlath = x 12,
• Olath = x 12,
• h =

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.

### L4 7/16 Octahedron Dome

 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 (αstrut):
• 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)
• 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

#### L4 7/16 Octahedron Dome Calculator

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

d = , lhole =
(Edit numbers & hit TAB to recalculate)

• Alath = x 28,
• Blath = x 16,
• Clath = x 24,
• Dlath = x 40,
• Elath = x 16,
• Flath = x 24,
• Glath = x 40,
• Hlath = x 16,
• Ilath = x 24,
• Jlath = x 16,
• Klath = x 4,
• Llath = x 12,
• Mlath = x 24,
• Nlath = x 12,
• Olath = x 12,
• h =

### L4 9/16 Octahedron Dome

 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 (αstrut):
• 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)
• 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

#### L4 9/16 Octahedron Dome Calculator

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

d = , lhole =
(Edit numbers & hit TAB to recalculate)

• Alath = x 68,
• Blath = x 40,
• Clath = x 32,
• Dlath = x 56,
• Elath = x 32,
• Flath = x 32,
• Glath = x 56,
• Hlath = x 32,
• Ilath = x 24,
• Jlath = x 32,
• Klath = x 20,
• Llath = x 12,
• Mlath = x 24,
• Nlath = x 16,
• Olath = x 12,
• h =

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

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Creative Commons (CC) BY-SA-NC 2005-2017, developed, designed and written by René K. Müller
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