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Geodesic Dome Notes & Calculator

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

7V Octahedron Dome


Geodesic 7V Octahedron Dome (front view)

Geodesic 7V Octahedron Dome (bird view)
  • vertices/connectors: 113
    • 4 x 3-way
    • 25 x 4-way
    • 84 x 6-way

  • 7V Octahedron Dome Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 16: 0.16496 (4.73°)
    • B x 24: 0.19598 (5.62°)
    • C x 16: 0.21494 (6.17°)
    • D x 12: 0.23250 (6.68°)
    • E x 24: 0.23440 (6.73°)
    • F x 24: 0.26112 (7.50°)
    • G x 16: 0.26224 (7.53°)
    • H x 24: 0.26495 (7.61°)
    • I x 24: 0.27001 (7.76°)
    • J x 24: 0.28228 (8.11°)
    • K x 8: 0.28284 (8.13°)
    • L x 24: 0.30770 (8.85°)
    • M x 12: 0.30861 (8.88°)
    • N x 24: 0.31244 (8.99°)
    • O x 24: 0.32892 (9.47°)
    • P x 12: 0.34300 (9.88°)
    • total 308 struts (16 kinds)1)
    • strut variance 107.9%
  • faces: 196 (3-sided)
    • A-A-D x 12 (45.21°, 45.21°, 89.59°)
    • B-B-D x 12 (53.62°, 53.62°, 72.76°)
    • B-C-H x 24 (46.78°, 53.04°, 80.18°)
    • E-F-H x 24 (52.91°, 62.69°, 64.40°)
    • E-G-J x 24 (50.83°, 60.14°, 69.03°)
    • F-F-M x 12 (53.77°, 53.77°, 72.45°)
    • I-I-K x 12 (58.42°, 58.42°, 63.16°)
    • I-J-N x 24 (53.71°, 57.44°, 68.85°)
    • L-L-M x 12 (59.90°, 59.90°, 60.19°)
    • L-N-O x 24 (57.28°, 58.66°, 64.06°)
    • O-O-P x 12 (58.57°, 58.57°, 62.86°)
    • P-P-P x 4 (60.00°, 60.00°, 60.00°)
    • 12 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

7V Octahedron Dome Calculator


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

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

  • Alath = x 16,
  • Blath = x 24,
  • Clath = x 16,
  • Dlath = x 12,
  • Elath = x 24,
  • Flath = x 24,
  • Glath = x 16,
  • Hlath = x 24,
  • Ilath = x 24,
  • Jlath = x 24,
  • Klath = x 8,
  • Llath = x 24,
  • Mlath = x 12,
  • Nlath = x 24,
  • Olath = x 24,
  • Plath = x 12,
  • h =


8V Octahedron Dome


Geodesic 8V Octahedron Dome (front view)

Geodesic 8V Octahedron Dome (bird view)
  • vertices/connectors: 145
    • 4 x 3-way
    • 29 x 4-way
    • 112 x 6-way

  • 8V Octahedron Dome Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 16: 0.14178 (4.07°)
    • B x 24: 0.16439 (4.71°)
    • C x 16: 0.17961 (5.15°)
    • D x 24: 0.19238 (5.52°)
    • E x 12: 0.20000 (5.74°)
    • F x 24: 0.21272 (6.11°)
    • G x 16: 0.21823 (6.26°)
    • H x 24: 0.22192 (6.37°)
    • I x 24: 0.22504 (6.46°)
    • J x 24: 0.24197 (6.95°)
    • K x 24: 0.24229 (6.96°)
    • L x 16: 0.24437 (7.02°)
    • M x 24: 0.24915 (7.16°)
    • N x 24: 0.25786 (7.41°)
    • O x 12: 0.25820 (7.42°)
    • P x 24: 0.27685 (7.96°)
    • Q x 12: 0.27735 (7.97°)
    • R x 24: 0.28011 (8.05°)
    • S x 24: 0.29180 (8.39°)
    • T x 12: 0.30151 (8.67°)
    • total 400 struts (20 kinds)1)
    • strut variance 112.6%
  • faces: 256 (3-sided)
    • A-A-E x 12 (45.15°, 45.15°, 89.69°)
    • B-B-E x 12 (52.54°, 52.54°, 74.93°)
    • B-C-I x 24 (46.28°, 52.15°, 81.57°)
    • D-F-I x 24 (52.06°, 60.68°, 67.26°)
    • D-G-K x 24 (49.05°, 58.93°, 72.02°)
    • F-F-O x 12 (52.63°, 52.63°, 74.74°)
    • H-J-L x 24 (54.28°, 62.31°, 63.41°)
    • H-K-N x 24 (52.56°, 60.11°, 67.34°)
    • J-J-Q x 12 (55.04°, 55.04°, 69.91°)
    • M-M-O x 12 (58.80°, 58.80°, 62.40°)
    • M-N-R x 24 (55.00°, 57.97°, 67.03°)
    • P-P-Q x 12 (59.94°, 59.94°, 60.12°)
    • P-R-S x 24 (57.85°, 58.95°, 63.19°)
    • S-S-T x 12 (58.89°, 58.89°, 62.21°)
    • T-T-T x 4 (60.00°, 60.00°, 60.00°)
    • 15 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

8V Octahedron Dome Calculator


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

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

  • Alath = x 16,
  • Blath = x 24,
  • Clath = x 16,
  • Dlath = x 24,
  • Elath = x 12,
  • Flath = x 24,
  • Glath = x 16,
  • Hlath = x 24,
  • Ilath = x 24,
  • Jlath = x 24,
  • Klath = x 24,
  • Llath = x 16,
  • Mlath = x 24,
  • Nlath = x 24,
  • Olath = x 12,
  • Plath = x 24,
  • Qlath = x 12,
  • Rlath = x 24,
  • Slath = x 24,
  • Tlath = x 12,
  • h =


L4 Octahedron Dome


Geodesic L4 Octahedron Dome (front view)

Geodesic L4 Octahedron Dome (bird view)
  • vertices/connectors: 145
    • 4 x 3-way
    • 29 x 4-way
    • 112 x 6-way

  • L4 Octahedron Dome Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 64: 0.19603 (5.62°)
    • B x 24: 0.19991 (5.74°)
    • C x 24: 0.20044 (5.75°)
    • D x 48: 0.21266 (6.10°)
    • E x 24: 0.21671 (6.22°)
    • F x 24: 0.21746 (6.24°)
    • G x 48: 0.26105 (7.50°)
    • H x 24: 0.26433 (7.59°)
    • I x 24: 0.26899 (7.73°)
    • J x 24: 0.27316 (7.85°)
    • K x 12: 0.27590 (7.93°)
    • L x 12: 0.27686 (7.96°)
    • M x 24: 0.29180 (8.39°)
    • N x 12: 0.29886 (8.59°)
    • O x 12: 0.30151 (8.67°)
    • total 400 struts (15 kinds)1)
    • strut variance 53.8%
  • faces: 256 (3-sided)
    • A-A-K x 12 (45.27°, 45.27°, 89.47°)
    • A-B-J x 24 (45.78°, 46.96°, 87.27°)
    • A-D-H x 24 (47.00°, 52.53°, 80.47°)
    • A-E-G x 24 (47.32°, 54.37°, 78.32°)
    • B-B-K x 12 (46.36°, 46.36°, 87.28°)
    • C-D-G x 24 (48.74°, 52.92°, 78.34°)
    • C-E-H x 24 (48.00°, 53.47°, 78.53°)
    • D-D-L x 12 (49.39°, 49.39°, 81.22°)
    • D-F-J x 24 (49.80°, 51.36°, 78.84°)
    • F-F-L x 12 (50.46°, 50.46°, 79.07°)
    • G-G-N x 12 (55.08°, 55.08°, 69.83°)
    • G-I-M x 24 (55.32°, 57.91°, 66.78°)
    • I-I-N x 12 (56.25°, 56.25°, 67.50°)
    • M-M-O x 12 (58.89°, 58.89°, 62.21°)
    • O-O-O x 4 (60.00°, 60.00°, 60.00°)
    • 15 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

L4 Octahedron Dome Calculator


Geodesic L4 Octahedron Dome (Human is 170cm/5'7")

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

  • Alath = x 64,
  • Blath = x 24,
  • Clath = x 24,
  • Dlath = x 48,
  • Elath = x 24,
  • Flath = x 24,
  • Glath = x 48,
  • Hlath = x 24,
  • Ilath = x 24,
  • Jlath = x 24,
  • Klath = x 12,
  • Llath = x 12,
  • Mlath = x 24,
  • Nlath = x 12,
  • Olath = x 12,
  • h =

Now the advantage of L3 vs 4V is more apparent, the L3 has various almost even horizontal bases where 4V has only one at 1/2 height.

So, let's explore 7/16 and 9/16 variants as well.

L4 7/16 Octahedron Dome


Geodesic L4 7/16 Octahedron Dome (front view)

Geodesic L4 7/16 Octahedron Dome (bird view)
  • vertices/connectors: 113
    • 4 x 3-way
    • 25 x 4-way
    • 84 x 6-way

  • L4 7/16 Octahedron Dome Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 28: 0.19603 (5.62°)
    • B x 16: 0.19991 (5.74°)
    • C x 24: 0.20044 (5.75°)
    • D x 40: 0.21266 (6.10°)
    • E x 16: 0.21671 (6.22°)
    • F x 24: 0.21746 (6.24°)
    • G x 40: 0.26105 (7.50°)
    • H x 16: 0.26433 (7.59°)
    • I x 24: 0.26899 (7.73°)
    • J x 16: 0.27316 (7.85°)
    • K x 4: 0.27590 (7.93°)
    • L x 12: 0.27686 (7.96°)
    • M x 24: 0.29180 (8.39°)
    • N x 12: 0.29886 (8.59°)
    • O x 12: 0.30151 (8.67°)
    • total 308 struts (15 kinds)1)
    • strut variance 53.8%
  • faces: 196 (3-sided)
    • A-A-K x 4 (45.27°, 45.27°, 89.47°)
    • A-B-J x 16 (45.78°, 46.96°, 87.27°)
    • A-D-H x 16 (47.00°, 52.53°, 80.47°)
    • A-E-G x 16 (47.32°, 54.37°, 78.32°)
    • B-B-K x 4 (46.36°, 46.36°, 87.28°)
    • C-D-G x 24 (48.74°, 52.92°, 78.34°)
    • C-E-H x 16 (48.00°, 53.47°, 78.53°)
    • D-D-L x 12 (49.39°, 49.39°, 81.22°)
    • D-F-J x 16 (49.80°, 51.36°, 78.84°)
    • F-F-L x 12 (50.46°, 50.46°, 79.07°)
    • G-G-N x 8 (55.08°, 55.08°, 69.83°)
    • G-I-M x 24 (55.32°, 57.91°, 66.78°)
    • I-I-N x 12 (56.25°, 56.25°, 67.50°)
    • M-M-O x 12 (58.89°, 58.89°, 62.21°)
    • O-O-O x 4 (60.00°, 60.00°, 60.00°)
    • 15 kinds of faces2)
  • diameter: 2.000, radius: 1.000
  • height: 0.805 or 40.25% 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

L4 7/16 Octahedron Dome Calculator


Geodesic L4 7/16 Octahedron Dome (Human is 170cm/5'7")

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

  • Alath = x 28,
  • Blath = x 16,
  • Clath = x 24,
  • Dlath = x 40,
  • Elath = x 16,
  • Flath = x 24,
  • Glath = x 40,
  • Hlath = x 16,
  • Ilath = x 24,
  • Jlath = x 16,
  • Klath = x 4,
  • Llath = x 12,
  • Mlath = x 24,
  • Nlath = x 12,
  • Olath = x 12,
  • h =


L4 9/16 Octahedron Dome


Geodesic L4 9/16 Octahedron Dome (front view)

Geodesic L4 9/16 Octahedron Dome (bird view)
  • vertices/connectors: 173
    • 29 x 4-way
    • 4 x 5-way
    • 140 x 6-way

  • L4 9/16 Octahedron Dome Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 68: 0.19603 (5.62°)
    • B x 40: 0.19991 (5.74°)
    • C x 32: 0.20044 (5.75°)
    • D x 56: 0.21266 (6.10°)
    • E x 32: 0.21671 (6.22°)
    • F x 32: 0.21746 (6.24°)
    • G x 56: 0.26105 (7.50°)
    • H x 32: 0.26433 (7.59°)
    • I x 24: 0.26899 (7.73°)
    • J x 32: 0.27316 (7.85°)
    • K x 20: 0.27590 (7.93°)
    • L x 12: 0.27686 (7.96°)
    • M x 24: 0.29180 (8.39°)
    • N x 16: 0.29886 (8.59°)
    • O x 12: 0.30151 (8.67°)
    • total 488 struts (15 kinds)1)
    • strut variance 53.8%
  • faces: 316 (3-sided)
    • A-A-K x 20 (45.27°, 45.27°, 89.47°)
    • A-B-J x 32 (45.78°, 46.96°, 87.27°)
    • A-D-H x 32 (47.00°, 52.53°, 80.47°)
    • A-E-G x 32 (47.32°, 54.37°, 78.32°)
    • B-B-K x 20 (46.36°, 46.36°, 87.28°)
    • C-D-G x 24 (48.74°, 52.92°, 78.34°)
    • C-E-H x 32 (48.00°, 53.47°, 78.53°)
    • D-D-L x 12 (49.39°, 49.39°, 81.22°)
    • D-F-J x 32 (49.80°, 51.36°, 78.84°)
    • F-F-L x 12 (50.46°, 50.46°, 79.07°)
    • G-G-N x 16 (55.08°, 55.08°, 69.83°)
    • G-I-M x 24 (55.32°, 57.91°, 66.78°)
    • I-I-N x 12 (56.25°, 56.25°, 67.50°)
    • M-M-O x 12 (58.89°, 58.89°, 62.21°)
    • O-O-O x 4 (60.00°, 60.00°, 60.00°)
    • 15 kinds of faces2)
  • diameter: 2.000, radius: 1.000
  • height: 1.211 or 60.57% 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

L4 9/16 Octahedron Dome Calculator


Geodesic L4 9/16 Octahedron Dome (Human is 170cm/5'7")

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

  • Alath = x 68,
  • Blath = x 40,
  • Clath = x 32,
  • Dlath = x 56,
  • Elath = x 32,
  • Flath = x 32,
  • Glath = x 56,
  • Hlath = x 32,
  • Ilath = x 24,
  • Jlath = x 32,
  • Klath = x 20,
  • Llath = x 12,
  • Mlath = x 24,
  • Nlath = x 16,
  • Olath = x 12,
  • h =


The L4 6/16 and 10/16 Octahedron Dome would be also possible, but the leveling gets already bigger as you see.


L4 6/16 Octahedron Dome

L4 10/16 Octahedron Dome


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