Icosidodecahedron

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Icosidodecahedron
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Icosidodecahedron.jpg
Icosidodecahedron


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TypeArchimedean
Faces20 triangles
12 pentagons
Edges60
Vertices30
Vertex configuration3,5,3,5
Symmetry groupicosahedral (Ih)
Dual polyhedronrhombic triacontahedron
Propertiesconvex, 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.

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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.

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

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