Nonconvex great rhombicosidodecahedron

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}
Wythoff symbol 5/3 3 | 2
Symmetry group Ih, [5,3], *532
Index references U67, C84, W105
Bowers acronym Qrid

3.4.5/3.4
(Vertex figure)

Great deltoidal hexecontahedron
(dual polyhedron)

In geometry, the nonconvex great rhombicosidodecahedron is a nonconvex uniform polyhedron, indexed as U67. It is also called the quasirhombicosidodecahedron. It is given a Schläfli symbol t0,2{5/3,3}. Its vertex figure is a crossed quadrilateral.

This model shares the name with the convex great rhombicosidodecahedron, also known as the truncated icosidodecahedron.

Contents

Cartesian coordinates

Cartesian coordinates for the vertices of a nonconvex great rhombicosidodecahedron are all the even permutations of

(±1/τ2, 0, ±(2−1/τ))
(±1, ±1/τ3, ±1)
(±1/τ, ±1/τ2, ±2/τ)

where τ = (1+√5)/2 is the golden ratio (sometimes written φ).

Related polyhedra

It shares its vertex arrangement with the truncated great dodecahedron, and with the uniform compounds of 6 or 12 pentagonal prisms. It additionally shares its edge arrangement with the great dodecicosidodecahedron (having the triangular and pentagrammic faces in common), and the great rhombidodecahedron (having the square faces in common).


Nonconvex great rhombicosidodecahedron

Great dodecicosidodecahedron

Great rhombidodecahedron

Truncated great dodecahedron

Compound of six pentagonal prisms

Compound of twelve pentagonal prisms

See also

External links