# Small complex icosidodecahedron

(Redirected from Small complex icosidodecacron)
Small complex icosidodecahedron
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
(3/2.5)5
(3.5)5/3
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

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.

 Icosahedron Great dodecahedron Compound