Great complex icosidodecahedron

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Great complex icosidodecahedron
Great complex icosidodecahedron.png
Type Uniform star polyhedron
Elements F = 32, E = 60 (30x2)
V = 12 (χ = -16)
Faces by sides 20{3}+12{5/2}
Wythoff symbol 5 | 3 5/3
Symmetry group Ih, [5,3], *532
Index references U-, C-, W-
Dual polyhedron Great complex icosidodecacron
Vertex figure Great complex icosidodecahedron verf.png
Bowers acronym Gacid

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.

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

As a compound[edit]

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.

Its two-dimensional analogue would be the compound of a regular pentagon, {5}, and regular pentagram, {5/2}.

Compound polyhedron
Small stellated dodecahedron.png Great icosahedron.png Great complex icosidodecahedron.png
Small stellated dodecahedron Great icosahedron Compound
Compound polygon
Pentagon.svg Star polygon 5-2.svg Complete graph K5.svg
Pentagon Pentagram Compound

See also[edit]