- Uniform great rhombicosidodecahedron
In

geometry , the**uniform great rhombicosidodecahedron**is a nonconvexuniform polyhedron , indexed as U_{67}. It is also called the "quasirhombicosidodecahedron".This model shares the name with the convex

great rhombicosidodecahedron , which is also called the "truncated icosidodecahedron". Because of this confusion the word**uniform**was added to this article name.It shares its vertex arrangement with the

truncated great dodecahedron , and with the uniform compounds of 6 or 12 pentagonal prisms.**Cartesian coordinates**Cartesian coordinates for the vertices of a uniform great rhombicosidodecahedron are all the even permutations of: (±1/τ

^{2}, 0, ±(2−1/τ)): (±1, ±1/τ^{3}, ±1): (±1/τ, ±1/τ^{2}, ±2/τ)where τ = (1+√5)/2 is the

golden ratio (sometimes written φ).**See also***

List of uniform polyhedra **External links***

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**Nonconvex great rhombicosidodecahedron**— Type Uniform star polyhedron Elements F = 62, E = 120 V = 60 (χ = 2) Faces by sides 20{3}+30{4}+12{5/2} … Wikipedia**Uniform star polyhedron**— A display of uniform polyhedra at the Science Museum in London … Wikipedia**Great dodecicosidodecahedron**— In geometry, the great dodecicosidodecahedron is a nonconvex uniform polyhedron, indexed as U61.It shares the vertex and edge arrangement, as well as its triangular and pentagrammic faces, with the uniform great rhombicosidodecahedron. See also * … Wikipedia**Great rhombidodecahedron**— In geometry, the great rhombidodecahedron is a nonconvex uniform polyhedron, indexed as U73.It shares the vertex and edge arrangement, as well as its square faces, with the uniform great rhombicosidodecahedron. See also * List of uniform… … Wikipedia**Rhombicosidodecahedron**— The rhombicosidodecahedron, or small rhombicosidodecahedron, is an Archimedean solid. It has 20 regular triangular faces, 30 regular square faces, 12 regular pentagonal faces, 60 vertices and 120 edges.The name rhombicosidodecahedron refers to… … Wikipedia**Great dirhombicosidodecahedron**— Type Uniform star polyhedron Elements F = 124, E = 240 V = 60 (χ = −56) Faces by sides 40{3}+60{4}+24{5/2} … Wikipedia**Truncated great dodecahedron**— Type Uniform star polyhedron Elements F = 24, E = 90 V = 60 (χ = −6) Faces by sides 12{5/2}+12{10} Wythof … Wikipedia**Convex uniform honeycombs in hyperbolic space**— The {5,3,4} honeycomb in 3D hyperbolic space, viewed in perspective In geometry, a convex uniform honeycomb is a tessellation of convex uniform polyhedron cells. In 3 dimensional hyperbolic space there are nine Coxeter group f … Wikipedia**Truncated great icosahedron**— Type Uniform star polyhedron Elements F = 32, E = 90 V = 60 (χ = 2) Faces by sides 12{5/2}+20{6} Wythoff symb … Wikipedia**Small complex rhombicosidodecahedron**— Type Uniform star polyhedron Elements F = 62, E = 120 (60x2) V = 20 (χ = 38) Faces by sides 20{3}+12{5/2}+30{4} … Wikipedia