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Geodesic Polyhedra

written by Rene K. Mueller, Copyright (c) 2007, last updated Fri, February 25, 2022

Geodesic Truncated Icosahedron

Truncated Icosahedron


Truncated Icosahedron
  • Uniform Polyhedron: U25
  • Archimedean Solid: A11
  • Wythoff symbol: 2 5|3
  • Symmetry Group: icosahedral
  • Vertex Configuration: {6, 6, 5}
  • Dual: pentakis dodecahedron
  • V: s3 / 4 * (125 + 43 * √5)
  • A: s2 * 3 * (10 * √3 + √5 * √(5 + 2 * √5))
  • rinner: s * 9/872 * (21 + √5) * √(58 + 18 * √5)
  • router: s / 4 * √(58 + 18 * √5)
  • Vertices/Connectors: 60 (3-way)
  • Faces: 32
    • 12 x 5-sided
    • 20 x 6-sided
  • Edges/Struts:
    • A x 90: 0.40355

Geodesic Truncated Icosahedron L1


Geodesic Truncated Icosahedron L1
  • Vertices/Connectors: 92
    • 12 x 5-way
    • 80 x 6-way
  • Faces: 180 (3-sided)
  • Edges/Struts:
    • A x 60: 0.34862
    • B x 90: 0.40355
    • C x 120: 0.41241
    • total 270 struts (3 kinds)
    • strut variance 18.1%


Geodesic Truncated Icosahedron Dome L1


Geodesic Truncated Icosahedron Dome L1

Geodesic Truncated Icosahedron Dome L1
  • Vertices/Connectors: 46
    • 15 x 4-way
    • 6 x 5-way
    • 25 x 6-way
  • Faces: 75 (3-sided)

  • Truncated Icosahedron Dome L1 Construction Map
  • Edges/Struts:
    • A x 30: 0.34862
    • B x 40: 0.40355
    • C x 50: 0.41241
    • total 120 struts (3 kinds)
    • strut variance 18.1%

d= A= x 30, B= x 40, C= x 50,
The L1 seems like having two straight hemisphere lines, at 3/7 and 4/7 approximately, looks like a Icosahedron 3V.

Geodesic Truncated Icosahedron L2


Geodesic Truncated Icosahedron L2
  • Vertices/Connectors: 362
    • 12 x 5-way
    • 350 x 6-way
  • Faces: 720 (3-sided)
  • Edges/Struts:
    • A x 120: 0.17498
    • B x 120: 0.17741
    • C x 180: 0.20282
    • D x 60: 0.20491
    • E x 120: 0.20621
    • F x 240: 0.20732
    • G x 240: 0.21063
    • total 1080 struts (7 kinds)
    • strut variance 20.6%


Geodesic Truncated Icosahedron Dome L2


Geodesic Truncated Icosahedron Dome L2

Geodesic Truncated Icosahedron Dome L2
  • Vertices/Connectors: 196
    • 30 x 4-way
    • 6 x 5-way
    • 160 x 6-way
  • Faces: 360 (3-sided)

  • Truncated Icosahedron Dome L2 Construction Map
  • Edges/Struts:
    • A x 60: 0.17498
    • B x 60: 0.17741
    • C x 90: 0.20282
    • D x 30: 0.20491
    • E x 65: 0.20621
    • F x 120: 0.20732
    • G x 130: 0.21063
    • total 555 struts (7 kinds)
    • strut variance 20.6%

d= A= x 60, B= x 60, C= x 90, D= x 30, E= x 65, F= x 120, G= x 130,

Geodesic Truncated Icosahedron L2T


Geodesic Truncated Icosahedron L2T
  • Vertices/Connectors: 542
    • 270 x 4-way
    • 180 x 6-way
    • 12 x 10-way
    • 80 x 12-way
  • Faces: 1080 (3-sided)
  • Edges/Struts:
    • A x 60: 0.09684
    • B x 120: 0.11337
    • C x 240: 0.12015
    • D x 120: 0.12264
    • E x 120: 0.17498
    • F x 60: 0.19033
    • G x 180: 0.20282
    • H x 240: 0.20732
    • I x 120: 0.22432
    • J x 240: 0.23636
    • K x 120: 0.24155
    • total 1620 struts (11 kinds)
    • strut variance 149.5%


Geodesic Truncated Icosahedron Dome L2T


Geodesic Truncated Icosahedron Dome L2T

Geodesic Truncated Icosahedron Dome L2T
  • Vertices/Connectors: 289
    • 12 x 3-way
    • 141 x 4-way
    • 88 x 6-way
    • 8 x 7-way
    • 4 x 10-way
    • 36 x 12-way
  • Faces: 540 (3-sided)

  • Truncated Icosahedron Dome L2T Construction Map
  • Edges/Struts:
    • A x 32: 0.09684
    • B x 60: 0.11337
    • C x 120: 0.12015
    • D x 64: 0.12264
    • E x 64: 0.17498
    • F x 32: 0.19033
    • G x 92: 0.20282
    • H x 120: 0.20732
    • I x 60: 0.22432
    • J x 120: 0.23636
    • K x 64: 0.24155
    • total 828 struts (11 kinds)
    • strut variance 149.5%

d= A= x 32, B= x 60, C= x 120, D= x 64, E= x 64, F= x 32, G= x 92, H= x 120, I= x 60, J= x 120, K= x 64,


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