Icosidodecahedron - Definition and Overview

Icosidodecahedron
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Type	Archimedean
Faces	20 triangles 12 pentagons
Edges	60
Vertices	30
Vertex configuration	3,5,3,5
Symmetry group	icosahedral (Ih)
Dual polyhedron	rhombic triacontahedron
Properties	convex, quasi-regular (vertex/edge uniform)

An icosidodecahedron is a polyhedron with twenty triangular faces and twelve pentagonal faces. An icosidodecahedron has 30 identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon. As such it is one of the Archimedean solids and more particularly, one of the quasi-regular polyhedra.

Icosidodecahedron_flat.png
image:icosidodecahedron flat.png

An icosidodecahedron has icosahedral symmetry, and its first stellation is the compound of a dodecahedron and its dual icosahedron, with the vertices of the icosahedron located at the midpoints of the edges of either. Canonical coordinates for the vertices of an icosidodecahedron are the cyclic permutations of (0,0,±τ), (±1/2, ±τ/2, ±(1+τ)/2), where τ is the Golden mean, (1+√5)/2. Its dual polyhedron is the rhombic triacontahedron. An icosidodecahedron can be split along several planes to form pentagonal rotundae, which belong among the Johnson solids.

Using the standard nomenclature used for the Johnson solids, an icosidodecahedron would be called a Pentagonal gyrobirotunda.

See also

• cuboctahedron
• dodecahedron
• icosahedron
• rhombicosidodecahedron
• truncated icosidodecahedron

External links

• The Uniform Polyhedra (http://www.mathconsult.ch/showroom/unipoly/)
• Virtual Reality Polyhedra (http://www.georgehart.com/virtual-polyhedra/vp.html) The Encyclopedia of Polyhedra