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# Geodesic Dome Notes & Calculator

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

## The Truncated Octahedron

 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)
• rinner: s * 9/20 * √10
• router: s / 2 * √10

s = , V = , A = , rinner = , router = , ravg =

### Preparing the Truncated Octahedron

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.

### 1V/L1 Truncated Octahedron Dome

 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 (αstrut):
• 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)
• 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

#### 1V Truncated Octahedron Dome Calculator

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

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

• Alath = x 16,
• Blath = x 2,
• Clath = x 18,
• Dlath = x 24,
• h =

### 2V/L2 Truncated Octahedron Dome

 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 (αstrut):
• 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)
• 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

#### 2V Truncated Octahedron Dome Calculator

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

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

• Alath = x 32,
• Blath = x 24,
• Clath = x 40,
• Dlath = x 12,
• Elath = x 24,
• Flath = x 48,
• Glath = x 48,
• h =

### 3V Truncated Octahedron Dome

 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 (αstrut):
• 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)
• 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

#### 3V Truncated Octahedron Dome Calculator

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

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

• Alath = x 32,
• Blath = x 16,
• Clath = x 24,
• Dlath = x 24,
• Elath = x 24,
• Flath = x 40,
• Glath = x 12,
• Hlath = x 24,
• Ilath = x 20,
• Jlath = x 24,
• Klath = x 96,
• Llath = x 48,
• Mlath = x 24,
• Nlath = x 48,
• Olath = x 48,
• h =

### 4V Truncated Octahedron Dome

 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 (αstrut):
• 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)
• 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

#### 4V Truncated Octahedron Dome Calculator

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

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

• Alath = x 32,
• Blath = x 24,
• Clath = x 24,
• Dlath = x 32,
• Elath = x 24,
• Flath = x 24,
• Glath = x 24,
• Hlath = x 24,
• Ilath = x 40,
• Jlath = x 36,
• Klath = x 24,
• Llath = x 40,
• Mlath = x 48,
• Nlath = x 24,
• Olath = x 12,
• Plath = x 48,
• Qlath = x 48,
• Rlath = x 24,
• Slath = x 48,
• Tlath = x 48,
• Ulath = x 48,
• Vlath = x 48,
• Wlath = x 48,
• Xlath = x 48,
• Ylath = x 48,
• h =

### L3 Truncated Octahedron Dome

 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 (αstrut):
• 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)
• 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

#### L3 Truncated Octahedron Dome Calculator

 Geodesic L3 Truncated 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 48,
• Flath = x 80,
• Glath = x 24,
• Hlath = x 48,
• Ilath = x 24,
• Jlath = x 24,
• Klath = x 48,
• Llath = x 6,
• Mlath = x 18,
• Nlath = x 24,
• Olath = x 96,
• Plath = x 96,
• Qlath = x 96,
• Rlath = x 48,
• Slath = x 48,
• h =

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