Small complex icosidodecahedron

Small complex icosidodecahedron
TypeUniform star polyhedron
ElementsF = 32, E = 60 (30x2)
V = 12 (χ = -16)
Faces by sides20{3}+12{5}
Wythoff symbol5 | 3/2 5
Symmetry groupIh, [5,3], *532
Index referencesU-, C-, W-
Dual polyhedronSmall complex icosidodecacron
Vertex figure
(3/2.5)5
(3.5)5/3
Bowers acronymCid

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.

Compound polyhedron
Icosahedron Great dodecahedron Compound

See also

References