Truncated icosidodecahedron

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Truncated icosidodecahedron
Missing image
Truncatedicosidodecahedron.jpg
Truncated icosidodecahedron


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TypeArchimedean
Faces30 squares
20 hexagons
12 decagons
Edges180
Vertices120
Vertex configuration4,6,10
Symmetry groupicosahedral (Ih)
Dual polyhedrondisdyakis triacontahedron
Propertiesconvex, semi-regular (vertex-uniform), zonohedron

The truncated icosidodecahedron, or great rhombicosidodecahedron, is an Archimedean solid. It has 30 regular square faces, 20 regular hexagonal faces, 12 regular decagonal faces, 120 vertices and 180 edges. Since each of its faces has point symmetry (equivalently, 180° rotational symmetry), the truncated icosidodecahedron is a zonohedron.

Missing image
Truncated_icosidodecahedron_flat.png
Truncated icosidodecahedron, flat

Note that the name truncated icosidodecahedron may be a little misleading. If you truncate an icosidodecahedron by cutting the corners off, you do not get an actual regular truncated icosidodecahedron: some of the faces will be irregular polygons. However, the resulting figure is topologically equivalent to truncated icosidodecahedron and can always be deformed until the faces are regular. The alternative name great rhombicosidodecahedron refers to the fact that the 30 square faces lie in the same planes as the 30 faces of the rhombic triacontahedron which is dual to the icosidodecahedron. Compare to small rhombicosidodecahedron.

Canonical coordinates for the vertices of a truncated icosidodecahedron centered at the origin are all the even permutations of (±1/τ, ±1/τ, ±(3+τ)), (±2/τ, ±τ, ±(1+2τ)), (±1/τ, ±τ2, ±(-1+3τ)), (±(-1+2τ), ±2, ±(2+τ)) and (±τ, ±3, ±2τ), where τ = (1+√5)/2 is the golden mean.

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