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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 10/21 Icosahedron Dome


Geodesic 7V 10/21 Icosahedron Dome (front view)

Geodesic 7V 10/21 Icosahedron Dome (bird view)
  • vertices/connectors: 246
    • 35 x 4-way
    • 6 x 5-way
    • 205 x 6-way

  • 7V 10/21 Icosahedron Dome Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 30: 0.13774 (3.95°)
    • B x 60: 0.15197 (4.36°)
    • C x 30: 0.15664 (4.49°)
    • D x 30: 0.16154 (4.63°)
    • E x 60: 0.16480 (4.73°)
    • F x 30: 0.17066 (4.90°)
    • G x 60: 0.17098 (4.90°)
    • H x 60: 0.17132 (4.91°)
    • I x 50: 0.17353 (4.98°)
    • J x 70: 0.17585 (5.04°)
    • K x 50: 0.18155 (5.21°)
    • L x 30: 0.18161 (5.21°)
    • M x 50: 0.18237 (5.23°)
    • N x 60: 0.18548 (5.32°)
    • O x 30: 0.18791 (5.39°)
    • total 700 struts (15 kinds)1)
    • strut variance 36.5%
  • faces: 455 (3-sided)
    • A-A-D x 30 (54.10°, 54.10°, 71.81°)
    • B-B-D x 30 (57.91°, 57.91°, 64.18°)
    • B-C-H x 60 (55.01°, 57.57°, 67.41°)
    • E-F-J x 60 (56.76°, 60.03°, 63.21°)
    • E-G-H x 60 (57.56°, 61.13°, 61.31°)
    • G-G-L x 30 (57.93°, 57.93°, 64.15°)
    • I-I-J x 20 (59.54°, 59.54°, 60.92°)
    • I-J-M x 50 (57.89°, 59.18°, 62.93°)
    • K-K-L x 25 (59.98°, 59.98°, 60.04°)
    • K-M-N x 50 (59.11°, 59.59°, 61.29°)
    • N-N-O x 30 (59.57°, 59.57°, 60.86°)
    • O-O-O x 10 (60.00°, 60.00°, 60.00°)
    • 12 kinds of faces2)
  • diameter: 2.000, radius: 1.000
  • height: 0.925 or 46.26% 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 10/21 Icosahedron Dome Calculator


Geodesic 7V 10/21 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 30,
  • Glath = x 60,
  • Hlath = x 60,
  • Ilath = x 50,
  • Jlath = x 70,
  • Klath = x 50,
  • Llath = x 30,
  • Mlath = x 50,
  • Nlath = x 60,
  • Olath = x 30,
  • h =


7V 11/21 Icosahedron Dome


Geodesic 7V 11/21 Icosahedron Dome (front view)

Geodesic 7V 11/21 Icosahedron Dome (bird view)
  • vertices/connectors: 281
    • 35 x 4-way
    • 6 x 5-way
    • 240 x 6-way

  • 7V 11/21 Icosahedron Dome Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 30: 0.13774 (3.95°)
    • B x 60: 0.15197 (4.36°)
    • C x 30: 0.15664 (4.49°)
    • D x 30: 0.16154 (4.63°)
    • E x 60: 0.16480 (4.73°)
    • F x 30: 0.17066 (4.90°)
    • G x 60: 0.17098 (4.90°)
    • H x 60: 0.17132 (4.91°)
    • I x 80: 0.17353 (4.98°)
    • J x 90: 0.17585 (5.04°)
    • K x 70: 0.18155 (5.21°)
    • L x 35: 0.18161 (5.21°)
    • M x 70: 0.18237 (5.23°)
    • N x 70: 0.18548 (5.32°)
    • O x 30: 0.18791 (5.39°)
    • total 805 struts (15 kinds)1)
    • strut variance 36.5%
  • faces: 525 (3-sided)
    • A-A-D x 30 (54.10°, 54.10°, 71.81°)
    • B-B-D x 30 (57.91°, 57.91°, 64.18°)
    • B-C-H x 60 (55.01°, 57.57°, 67.41°)
    • E-F-J x 60 (56.76°, 60.03°, 63.21°)
    • E-G-H x 60 (57.56°, 61.13°, 61.31°)
    • G-G-L x 30 (57.93°, 57.93°, 64.15°)
    • I-I-J x 40 (59.54°, 59.54°, 60.92°)
    • I-J-M x 70 (57.89°, 59.18°, 62.93°)
    • K-K-L x 35 (59.98°, 59.98°, 60.04°)
    • K-M-N x 70 (59.11°, 59.59°, 61.29°)
    • N-N-O x 30 (59.57°, 59.57°, 60.86°)
    • O-O-O x 10 (60.00°, 60.00°, 60.00°)
    • 12 kinds of faces2)
  • diameter: 2.000, radius: 1.000
  • height: 1.080 or 54.00% 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 11/21 Icosahedron Dome Calculator


Geodesic 7V 11/21 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 30,
  • Glath = x 60,
  • Hlath = x 60,
  • Ilath = x 80,
  • Jlath = x 90,
  • Klath = x 70,
  • Llath = x 35,
  • Mlath = x 70,
  • Nlath = x 70,
  • Olath = x 30,
  • h =


8V Icosahedron Dome


Geodesic 8V Icosahedron Dome (front view)

Geodesic 8V Icosahedron Dome (bird view)
  • vertices/connectors: 341
    • 40 x 4-way
    • 6 x 5-way
    • 295 x 6-way

  • 8V Icosahedron Dome Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 30: 0.11946 (3.42°)
    • B x 60: 0.13033 (3.74°)
    • C x 30: 0.13424 (3.85°)
    • D x 30: 0.14018 (4.02°)
    • E x 60: 0.14056 (4.03°)
    • F x 60: 0.14548 (4.17°)
    • G x 30: 0.14628 (4.19°)
    • H x 60: 0.14803 (4.24°)
    • I x 60: 0.14862 (4.26°)
    • J x 60: 0.15267 (4.38°)
    • K x 70: 0.15296 (4.39°)
    • L x 30: 0.15315 (4.39°)
    • M x 60: 0.15477 (4.44°)
    • N x 90: 0.15636 (4.48°)
    • O x 60: 0.16033 (4.60°)
    • P x 30: 0.16036 (4.60°)
    • Q x 70: 0.16088 (4.61°)
    • R x 60: 0.16300 (4.67°)
    • S x 30: 0.16465 (4.72°)
    • total 980 struts (19 kinds)1)
    • strut variance 37.7%
  • faces: 640 (3-sided)
    • A-A-D x 30 (54.08°, 54.08°, 71.83°)
    • B-B-D x 30 (57.45°, 57.45°, 65.09°)
    • B-C-H x 60 (54.73°, 57.24°, 68.03°)
    • E-F-H x 60 (57.24°, 60.49°, 62.28°)
    • E-G-J x 60 (56.05°, 59.67°, 64.28°)
    • F-F-N x 30 (57.49°, 57.49°, 65.02°)
    • I-J-N x 60 (57.45°, 60.02°, 62.52°)
    • I-K-L x 60 (58.06°, 60.90°, 61.04°)
    • K-K-P x 30 (58.39°, 58.39°, 63.23°)
    • M-M-N x 30 (59.66°, 59.66°, 60.69°)
    • M-N-Q x 60 (58.38°, 59.36°, 62.26°)
    • O-O-P x 30 (59.98°, 59.98°, 60.04°)
    • O-Q-R x 60 (59.32°, 59.69°, 60.99°)
    • R-R-S x 30 (59.67°, 59.67°, 60.65°)
    • S-S-S x 10 (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 Icosahedron Dome Calculator


Geodesic 8V 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 60,
  • Glath = x 30,
  • Hlath = x 60,
  • Ilath = x 60,
  • Jlath = x 60,
  • Klath = x 70,
  • Llath = x 30,
  • Mlath = x 60,
  • Nlath = x 90,
  • Olath = x 60,
  • Plath = x 30,
  • Qlath = x 70,
  • Rlath = x 60,
  • Slath = x 30,
  • h =


L4 Icosahedron Dome


Geodesic L4 Icosahedron Dome (front view)

Geodesic L4 Icosahedron Dome (bird view)
  • vertices/connectors: 341
    • 40 x 4-way
    • 6 x 5-way
    • 295 x 6-way

  • L4 Icosahedron Dome Construction Map
  • edges/struts & bending angles (αstrut):
    • A x 120: 0.13828 (3.96°)
    • B x 120: 0.13951 (4.00°)
    • C x 120: 0.14310 (4.10°)
    • D x 60: 0.14429 (4.14°)
    • E x 60: 0.14439 (4.14°)
    • F x 140: 0.15692 (4.50°)
    • G x 60: 0.15800 (4.53°)
    • H x 60: 0.15846 (4.54°)
    • I x 60: 0.16115 (4.62°)
    • J x 30: 0.16217 (4.65°)
    • K x 30: 0.16228 (4.65°)
    • L x 60: 0.16300 (4.67°)
    • M x 30: 0.16448 (4.72°)
    • N x 30: 0.16465 (4.72°)
    • total 980 struts (14 kinds)1)
    • strut variance 19.0%
  • faces: 640 (3-sided)
    • A-A-J x 30 (54.10°, 54.10°, 71.80°)
    • A-B-I x 60 (54.21°, 54.90°, 70.89°)
    • A-C-G x 60 (54.41°, 57.29°, 68.29°)
    • A-D-F x 60 (54.47°, 58.12°, 67.41°)
    • B-B-J x 30 (54.45°, 54.45°, 71.09°)
    • B-C-F x 60 (55.19°, 57.38°, 67.44°)
    • B-D-G x 60 (54.74°, 57.63°, 67.64°)
    • C-C-K x 30 (55.45°, 55.45°, 69.09°)
    • C-E-I x 60 (55.54°, 56.30°, 68.16°)
    • E-E-K x 30 (55.81°, 55.81°, 68.39°)
    • F-F-M x 30 (58.38°, 58.38°, 63.23°)
    • F-H-L x 60 (58.40°, 59.36°, 62.23°)
    • H-H-M x 30 (58.74°, 58.74°, 62.52°)
    • L-L-N x 30 (59.67°, 59.67°, 60.65°)
    • N-N-N x 10 (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 Icosahedron Dome Calculator


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

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

  • Alath = x 120,
  • Blath = x 120,
  • Clath = x 120,
  • Dlath = x 60,
  • Elath = x 60,
  • Flath = x 140,
  • Glath = x 60,
  • Hlath = x 60,
  • Ilath = x 60,
  • Jlath = x 30,
  • Klath = x 30,
  • Llath = x 60,
  • Mlath = x 30,
  • Nlath = x 30,
  • h =



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