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