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Geodesic Dome Notes & Calculator

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

5V 7/15 Icosahedron Dome


Geodesic 5V 7/15 Icosahedron Dome (front view)

Geodesic 5V 7/15 Icosahedron Dome (bird view)
  • vertices/connectors: 126
    • 25 x 4-way
    • 6 x 5-way
    • 95 x 6-way

  • 5V 7/15 Icosahedron Dome Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 30: 0.19815 (5.69°)
    • B x 60: 0.22569 (6.48°)
    • C x 30: 0.23160 (6.65°)
    • D x 30: 0.23179 (6.66°)
    • E x 50: 0.24509 (7.04°)
    • F x 10: 0.24535 (7.05°)
    • G x 60: 0.24724 (7.10°)
    • H x 50: 0.25517 (7.33°)
    • I x 30: 0.26160 (7.52°)
    • total 350 struts (9 kinds)1)
    • strut variance 32.1%
  • faces: 225 (3-sided)
    • A-A-D x 30 (54.19°, 54.19°, 71.61°)
    • B-B-D x 30 (59.10°, 59.10°, 61.80°)
    • B-C-G x 60 (56.13°, 58.44°, 65.43°)
    • E-E-F x 20 (59.96°, 59.96°, 60.08°)
    • E-G-H x 50 (58.37°, 59.18°, 62.45°)
    • H-H-I x 25 (59.17°, 59.17°, 61.67°)
    • I-I-I x 10 (60.00°, 60.00°, 60.00°)
    • 7 kinds of faces2)
  • diameter: 2.000, radius: 1.000
  • height: 0.896 or 44.78% 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

5V 7/15 Icosahedron Dome Calculator


Geodesic 5V 7/15 Icosahedron Dome (Human is 170cm/5'7")

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

  • Alath = x 30,
  • Blath = x 60,
  • Clath = x 30,
  • Dlath = x 30,
  • Elath = x 50,
  • Flath = x 10,
  • Glath = x 60,
  • Hlath = x 50,
  • Ilath = x 30,
  • h =

Cut optimization:
  • normalize Elath+Elath = 1.0, therefore Elath+Elath =
  • cuts:
    • 30 x (Alath+Glath):
    • 50 x (Blath+Flath):
    • 5 x (Blath+Blath):
    • 60 x (Clath+Dlath):
    • 30 x (Elath+Elath):
    • total 175 laths to cut


5V 8/15 Icosahedron Dome


Geodesic 5V 8/15 Icosahedron Dome (front view)

Geodesic 5V 8/15 Icosahedron Dome (bird view)
  • vertices/connectors: 151
    • 25 x 4-way
    • 6 x 5-way
    • 120 x 6-way

  • 5V 8/15 Icosahedron Dome Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 30: 0.19815 (5.69°)
    • B x 60: 0.22569 (6.48°)
    • C x 30: 0.23160 (6.65°)
    • D x 30: 0.23179 (6.66°)
    • E x 80: 0.24509 (7.04°)
    • F x 20: 0.24535 (7.05°)
    • G x 70: 0.24724 (7.10°)
    • H x 70: 0.25517 (7.33°)
    • I x 35: 0.26160 (7.52°)
    • total 425 struts (9 kinds)1)
    • strut variance 32.1%
  • faces: 275 (3-sided)
    • A-A-D x 30 (54.19°, 54.19°, 71.61°)
    • B-B-D x 30 (59.10°, 59.10°, 61.80°)
    • B-C-G x 60 (56.13°, 58.44°, 65.43°)
    • E-E-F x 40 (59.96°, 59.96°, 60.08°)
    • E-G-H x 70 (58.37°, 59.18°, 62.45°)
    • H-H-I x 35 (59.17°, 59.17°, 61.67°)
    • I-I-I x 10 (60.00°, 60.00°, 60.00°)
    • 7 kinds of faces2)
  • diameter: 2.000, radius: 1.000
  • height: 1.111 or 55.56% 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

5V 8/15 Icosahedron Dome Calculator


Geodesic 5V 8/15 Icosahedron Dome (Human is 170cm/5'7")

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

  • Alath = x 30,
  • Blath = x 60,
  • Clath = x 30,
  • Dlath = x 30,
  • Elath = x 80,
  • Flath = x 20,
  • Glath = x 70,
  • Hlath = x 70,
  • Ilath = x 35,
  • h =


6V Icosahedron Dome


Geodesic 6V Icosahedron Dome (front view)

Geodesic 6V Icosahedron Dome (bird view)
  • vertices/connectors: 196
    • 30 x 4-way
    • 6 x 5-way
    • 160 x 6-way

  • 6V Icosahedron Dome Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 30: 0.16257 (4.66°)
    • B x 60: 0.18191 (5.22°)
    • C x 30: 0.18738 (5.38°)
    • D x 30: 0.19048 (5.47°)
    • E x 60: 0.19801 (5.68°)
    • F x 90: 0.20282 (5.82°)
    • G x 130: 0.20591 (5.91°)
    • H x 65: 0.21535 (6.18°)
    • I x 60: 0.21663 (6.22°)
    • total 555 struts (9 kinds)1)
    • strut variance 33.2%
  • faces: 360 (3-sided)
    • A-A-D x 30 (54.14°, 54.14°, 71.72°)
    • B-B-D x 30 (58.42°, 58.42°, 63.15°)
    • B-C-F x 60 (55.40°, 58.00°, 66.60°)
    • E-F-G x 120 (57.95°, 60.24°, 61.81°)
    • G-G-H x 60 (58.46°, 58.46°, 63.08°)
    • H-I-I x 60 (59.63°, 60.18°, 60.18°)
    • 6 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

6V Icosahedron Dome Calculator


Geodesic 6V Icosahedron Dome (Human is 170cm/5'7")

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

  • Alath = x 30,
  • Blath = x 60,
  • Clath = x 30,
  • Dlath = x 30,
  • Elath = x 60,
  • Flath = x 90,
  • Glath = x 130,
  • Hlath = x 65,
  • Ilath = x 60,
  • h =


2V.3V Icosahedron Dome


Geodesic 2V.3V Icosahedron Dome (front view)

Geodesic 2V.3V Icosahedron Dome (bird view)
  • vertices/connectors: 196
    • 30 x 4-way
    • 6 x 5-way
    • 160 x 6-way

  • 2V.3V Icosahedron Dome Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 60: 0.18212 (5.22°)
    • B x 30: 0.18854 (5.41°)
    • C x 60: 0.18922 (5.43°)
    • D x 60: 0.18932 (5.43°)
    • E x 60: 0.19125 (5.49°)
    • F x 70: 0.20591 (5.91°)
    • G x 30: 0.21321 (6.12°)
    • H x 60: 0.21445 (6.16°)
    • I x 65: 0.21535 (6.18°)
    • J x 60: 0.21663 (6.22°)
    • total 555 struts (10 kinds)1)
    • strut variance 18.9%
  • faces: 360 (3-sided)
    • A-A-G x 30 (54.17°, 54.17°, 71.66°)
    • A-C-F x 60 (54.69°, 57.98°, 67.33°)
    • B-D-H x 60 (55.23°, 55.58°, 69.19°)
    • C-E-H x 60 (55.22°, 56.15°, 68.63°)
    • D-D-G x 30 (55.73°, 55.73°, 68.54°)
    • E-E-I x 30 (55.74°, 55.74°, 68.53°)
    • F-F-I x 30 (58.46°, 58.46°, 63.08°)
    • I-J-J x 60 (59.63°, 60.18°, 60.18°)
    • 8 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.3V Icosahedron Dome Calculator


Geodesic 2V.3V Icosahedron Dome (Human is 170cm/5'7")

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

  • Alath = x 60,
  • Blath = x 30,
  • Clath = x 60,
  • Dlath = x 60,
  • Elath = x 60,
  • Flath = x 70,
  • Glath = x 30,
  • Hlath = x 60,
  • Ilath = x 65,
  • Jlath = x 60,
  • h =

The 2V.3V has 10 kinds of strut lengths, and 18.7% strut variance - compared to 6V with 9 kinds and 33.3% variance. So, you might think about prefering more even triangles, choose 2V.3V or less struth kinds then the 6V.

3V.2V Icosahedron Dome

The 3V.2V Icosahedron could also be used to achieve the same amount of subdivision, yet, the 3V is a bit uneven around the base, and the 2nd stage of 2V doesn't even this again, so the base isn't even, yet, 7 kinds of struts. I won't list the details as I won't recommend 3V.2V over 2V.3V or 6V at all.


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