Truncated icosidodecahedron
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The truncated icosidodecahedron 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.
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Other names
Alternate interchangable names include:
- Great rhombicosidodecahedron
- Rhombitruncated icosidodecahedron
- Omnitruncated icosidodecahedron
The name truncated icosidodecahedron, originally give by Johannes Kepler is little misleading. If you truncate an icosidodecahedron by cutting the corners off, you do not get this uniform figure: some of the faces will be rectangles. However, the resulting figure is topologically equivalent to this and can always be deformed until the faces are regular.
The alternative name great rhombicosidodecahedron (as well as rhombitruncated icosidodecahedron) 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.
One unfortunate point of confusion. There is there's a nonconvex uniform polyhedron by the same name. See uniform great rhombicosidodecahedron.
Cartesian coordinates
Cartesian 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 ratio.
Image:Truncated icosidodecahedron flat.png
See also
- Spinning great rhombicosidodecahedron
- dodecahedron
- great truncated icosidodecahedron
- icosahedron
- icosidodecahedron
- truncated cuboctahedron
External links
- The Uniform Polyhedra
- Virtual Reality Polyhedra The Encyclopedia of Polyhedraes:Icosidodecaedro truncado