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# Geodesic Dome Notes

written by Rene K. Mueller, Copyright (c) 2005, 2006, 2007, last updated Thu, January 15, 2009

## The Cube

 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
• rinner: s / 2
• router: s / 2 * √3

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

### Preparing the Cube

 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.

### 1V/L1 Cube Dome

 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 (αstrut):
• 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°)
• height: 0.817 or 40.83% of diameter

#### 1V Cube Dome Calculator

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

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

• Alath = x 14,
• Blath = x 7,
• h =

### 2V/L2 Cube Dome

 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 (αstrut):
• 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)
• 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 Cube Dome Calculator

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

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

• Alath = x 28,
• Blath = x 24,
• Clath = x 14,
• Dlath = x 12,
• h =

### 3V Cube Dome

 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 (αstrut):
• 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)
• 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

#### 3V Cube Dome Calculator

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

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

• Alath = x 28,
• Blath = x 14,
• Clath = x 6,
• Dlath = x 18,
• Elath = x 24,
• Flath = x 24,
• Glath = x 14,
• Hlath = x 12,
• Ilath = x 24,
• Jlath = x 7,
• h =

### 4V Cube Dome

 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 (αstrut):
• 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)
• 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 Cube Dome Calculator

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

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

• Alath = x 28,
• Blath = x 24,
• Clath = x 24,
• Dlath = x 28,
• Elath = x 24,
• Flath = x 24,
• Glath = x 14,
• Hlath = x 24,
• Ilath = x 24,
• Jlath = x 24,
• Klath = x 12,
• Llath = x 24,
• Mlath = x 14,
• Nlath = x 12,
• h =

### L3 Cube Dome

 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 (αstrut):
• 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)
• 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 Cube Dome Calculator

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

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

• Alath = x 56,
• Blath = x 24,
• Clath = x 24,
• Dlath = x 48,
• Elath = x 24,
• Flath = x 24,
• Glath = x 28,
• Hlath = x 24,
• Ilath = x 24,
• Jlath = x 12,
• Klath = x 12,
• h =

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Creative Commons (CC) BY, NC 2005-2013, developed, designed and written by René K. Müller,
Graphics & illustrations made with Inkscape, Tgif, Gimp, PovRay, GD.pm