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Geodesic Dome Notes & Calculator

written by Rene K. Mueller, Copyright (c) 2005, 2006, 2007, last updated Sun, September 22, 2013

4V Octahedron Dome


Geodesic 4V Octahedron Dome (front view)

Geodesic 4V Octahedron Dome (bird view)
  • vertices/connectors: 41
    • 4 x 3-way
    • 13 x 4-way
    • 24 x 6-way

  • 4V Octahedron Dome Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 16: 0.32036 (9.22°)
    • B x 24: 0.43887 (12.68°)
    • C x 12: 0.44721 (12.92°)
    • D x 16: 0.45951 (13.28°)
    • E x 24: 0.51764 (15.00°)
    • F x 12: 0.57735 (16.78°)
    • total 104 struts (6 kinds)1)
    • strut variance 80.2%
  • faces: 64 (3-sided)
    • A-A-C x 12 (45.74°, 45.74°, 88.51°)
    • B-B-C x 12 (59.37°, 59.37°, 61.26°)
    • B-D-E x 24 (52.98°, 56.71°, 70.32°)
    • E-E-F x 12 (56.10°, 56.10°, 67.80°)
    • F-F-F x 4 (60.00°, 60.00°, 60.00°)
    • 5 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

4V Octahedron Dome Calculator


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

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

  • Alath = x 16,
  • Blath = x 24,
  • Clath = x 12,
  • Dlath = x 16,
  • Elath = x 24,
  • Flath = x 12,
  • h =


L3 Octahedron Dome


Geodesic L3 Octahedron Dome (front view)

Geodesic L3 Octahedron Dome (bird view)
  • vertices/connectors: 41
    • 4 x 3-way
    • 13 x 4-way
    • 24 x 6-way

  • L3 Octahedron Dome Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 32: 0.39018 (11.25°)
    • B x 24: 0.42291 (12.21°)
    • C x 24: 0.51764 (15.00°)
    • D x 12: 0.54120 (15.70°)
    • E x 12: 0.57735 (16.78°)
    • total 104 struts (5 kinds)1)
    • strut variance 48.0%
  • faces: 64 (3-sided)
    • A-A-D x 12 (46.09°, 46.09°, 87.81°)
    • A-B-C x 24 (47.72°, 53.31°, 78.96°)
    • B-B-D x 12 (50.22°, 50.22°, 79.56°)
    • C-C-E x 12 (56.10°, 56.10°, 67.80°)
    • E-E-E x 4 (60.00°, 60.00°, 60.00°)
    • 5 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

L3 Octahedron Dome Calculator


Geodesic L3 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 12,
  • Elath = x 12,
  • h =

The nice thing is here, that the L3 provides at 3/8 and 5/8 also an almost even base line.

L3 1/4 Octahedron Dome


Geodesic L3 3/8 Octahedron Dome (front view)

Geodesic L3 3/8 Octahedron Dome (bird view)
  • vertices/connectors: 25
    • 4 x 3-way
    • 9 x 4-way
    • 12 x 6-way

  • L3 3/8 Octahedron Dome Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 12: 0.39018 (11.25°)
    • B x 16: 0.42291 (12.21°)
    • C x 16: 0.51764 (15.00°)
    • D x 4: 0.54120 (15.70°)
    • E x 12: 0.57735 (16.78°)
    • total 60 struts (5 kinds)1)
    • strut variance 48.0%
  • faces: 36 (3-sided)
    • A-A-D x 4 (46.09°, 46.09°, 87.81°)
    • A-B-C x 16 (47.72°, 53.31°, 78.96°)
    • B-B-D x 4 (50.22°, 50.22°, 79.56°)
    • C-C-E x 8 (56.10°, 56.10°, 67.80°)
    • E-E-E x 4 (60.00°, 60.00°, 60.00°)
    • 5 kinds of faces2)
  • diameter: 2.000, radius: 1.000
  • height: 0.617 or 30.87% 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 3/8 Octahedron Dome Calculator


Geodesic L3 3/8 Octahedron Dome (Human is 170cm/5'7")

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

  • Alath = x 12,
  • Blath = x 16,
  • Clath = x 16,
  • Dlath = x 4,
  • Elath = x 12,
  • h =

Here again uneven base, for heavy construction leveling necessary.

L3 3/4 Octahedron Dome


Geodesic L3 5/8 Octahedron Dome (front view)

Geodesic L3 5/8 Octahedron Dome (bird view)
  • vertices/connectors: 53
    • 13 x 4-way
    • 4 x 5-way
    • 36 x 6-way

  • L3 5/8 Octahedron Dome Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 36: 0.39018 (11.25°)
    • B x 40: 0.42291 (12.21°)
    • C x 32: 0.51764 (15.00°)
    • D x 20: 0.54120 (15.70°)
    • E x 16: 0.57735 (16.78°)
    • total 144 struts (5 kinds)1)
    • strut variance 48.0%
  • faces: 92 (3-sided)
    • A-A-D x 20 (46.09°, 46.09°, 87.81°)
    • A-B-C x 32 (47.72°, 53.31°, 78.96°)
    • B-B-D x 20 (50.22°, 50.22°, 79.56°)
    • C-C-E x 16 (56.10°, 56.10°, 67.80°)
    • E-E-E x 4 (60.00°, 60.00°, 60.00°)
    • 5 kinds of faces2)
  • diameter: 2.000, radius: 1.000
  • height: 1.408 or 70.41% 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 5/8 Octahedron Dome Calculator


Geodesic L3 5/8 Octahedron Dome (Human is 170cm/5'7")

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

  • Alath = x 36,
  • Blath = x 40,
  • Clath = x 32,
  • Dlath = x 20,
  • Elath = x 16,
  • h =

Here again uneven base, for heavy construction leveling necessary.


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