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}. These shapes would share vertices, similarly to how its 3D equivalent shares edges.

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]