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# Geodesic Dome Notes

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

## The Octahedron

 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
• rinner: s / 6 * √6
• router: s / 2 * √2

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

### 1V/L1 Octahedron Dome

 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 (αstrut):
• A x 8: 1.41421 (45.00°)
• faces: 4 (3-sided)
• A-A-A x 4 (60.00°, 60.00°, 60.00°)
• height: 1.000 or 50.00% of diameter

#### 1V Octahedron Dome Calculator

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

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

• Alath = x 8,
• h =

### 2V/L2 Octahedron Dome

 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 (αstrut):
• 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)
• 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 Octahedron Dome Calculator

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

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

• Alath = x 16,
• Blath = x 12,
• h =

### 3V Octahedron Dome

 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 (αstrut):
• 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)
• 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 Octahedron Dome Calculator

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

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

• Alath = x 16,
• Blath = x 20,
• Clath = x 24,
• 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