Small complex icosidodecahedron

Small complex icosidodecahedron
Small complex icosidodecahedron
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-
Small complex icosidodecahedron
(3/2.5)5
(3.5)5/3
(Vertex figure)
Small complex icosidodecacron.png
Small complex icosidodecacron
(dual polyhedron)

In geometry, the small complex icosidodecahedron is a degenerate uniform star polyhedron. It has 32 faces (20 triangles and 12 pentagons), 60 (doubled) edges and 12 vertices. 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

It can be seen as a compound of the icosahedron {3,5} and the great dodecahedron {5,5/2} where all vertices and edges coincide. The small complex icosidodecahedron appears to be 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

References