Great complex icosidodecahedron

Degenerate uniform star polyhedron From Wikipedia, the free encyclopedia

Great complex icosidodecahedron

In geometry, the great complex icosidodecahedron is a degenerate uniform star polyhedron. It has 12 vertices, and 60 (doubled) edges, and 32 faces, 12 pentagrams and 20 triangles. All edges are doubled (making it degenerate), sharing 4 faces, but are considered as two overlapping edges as topological polyhedron.

Great complex icosidodecahedron
Thumb
TypeUniform star polyhedron
ElementsF = 32, E = 60 (30x2)
V = 12 (χ = -16)
Faces by sides20{3}+12{5/2}
Coxeter diagram
Wythoff symbol5 | 3 5/3
Symmetry groupIh, [5,3], *532
Index referencesU-, C-, W-
Dual polyhedronGreat complex icosidodecacron
Vertex figureThumb
(3.5/3)5
(3.5/2)5/3
Bowers acronymGacid

It can be constructed from a number of different vertex figures.

As a compound

The great complex icosidodecahedron can be considered a compound of the small stellated dodecahedron, {5/2,5}, and great icosahedron, {3,5/2}, sharing the same vertices and edges, while the second is hidden, being completely contained inside the first.

Compound polyhedron
Thumb Thumb Thumb
Small stellated dodecahedron Great icosahedron Compound

See also

References

  • Coxeter, Harold Scott MacDonald; Longuet-Higgins, M. S.; Miller, J. C. P. (1954), "Uniform polyhedra", Philosophical Transactions of the Royal Society of London. Series A. Mathematical and Physical Sciences, 246 (916): 401–450, Bibcode:1954RSPTA.246..401C, doi:10.1098/rsta.1954.0003, ISSN 0080-4614, JSTOR 91532, MR 0062446, S2CID 202575183 (Table 6, degenerate cases)
  • Weisstein, Eric W. "Great complex icosidodecahedron". MathWorld.
  • Klitzing, Richard. "3D uniform polyhedra o5/3x3o5*a and o3/2x5/2o5*a - gacid".
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