Small complex icosidodecahedron

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

In geometry, the small complex icosidodecahedron is a degenerate uniform star polyhedron. Its edges are doubled, making it degenerate. The star has 32 faces (20 triangles and 12 pentagons), 60 (doubled) edges and 12 vertices and 4 sharing faces. The faces in it are considered as two overlapping edges as topological polyhedron.

A small complex icosidodecahedron can be constructed from a number of different vertex figures.

As a compound[edit]

The small complex icosidodecahedron can be seen as a compound of the icosahedron {3,5} and the great dodecahedron {5,5/2} where all vertices are precise and edges coincide. The small complex icosidodecahedron resembles an icosahedron, because the great dodecahedron is completely contained inside the icosahedron.

Compound polyhedron
Icosahedron.png Great dodecahedron.png Small complex icosidodecahedron.png
Icosahedron Great dodecahedron Compound

See also[edit]