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Geodesic Dome Notes & Calculator

written by Rene K. Mueller, Copyright (c) 2005, 2006, 2007, last updated Tue, February 16, 2016

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°)
  • diameter: 2.000, radius: 1.000
  • 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)
  • 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

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)
  • 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

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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