Truncated icosidodecahedron
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.
Alternate interchangeable names include:
Great rhombicosidodecahedronRhombitruncated icosidodecahedronOmnitruncated icosidodecahedronThe name
truncated icosidodecahedron, originally given by
Johannes Kepler, is somewhat 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 is that there is a nonconvex uniform polyhedron of the same name. See
uniform great rhombicosidodecahedron.
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, ±τ
2, ±(-1+3τ)),: (±(-1+2τ), ±2, ±(2+τ)) and: (±τ, ±3, ±2τ),where τ = (1+√5)/2 is the
golden ratio.
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Truncated icosidodecahedron, flat |
*
Spinning great rhombicosidodecahedron*
dodecahedron*
great truncated icosidodecahedron*
icosahedron*
icosidodecahedron*
truncated cuboctahedron*
The Uniform Polyhedra*
Virtual Reality Polyhedra The Encyclopedia of Polyhedra
