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}
Coxeter diagram
Wythoff symbol	5/3 3 \| 2 5/2 3/2 \| 2
Symmetry group	I_h, [5,3], *532
Index references	U₆₇, C₈₄, W₁₀₅
Dual polyhedron	Great deltoidal hexecontahedron
Vertex figure	3.4.5/3.4
Bowers acronym	Qrid

In geometry, the nonconvex great rhombicosidodecahedron is a nonconvex uniform polyhedron, indexed as U₆₇. It has 62 faces (20 triangles, 30 squares and 12 pentagrams), 120 edges, and 60 vertices. It is also called the quasirhombicosidodecahedron. It is given a Schläfli symbol $rr{.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}5⁄3,3}.$ Its vertex figure is a crossed quadrilateral.

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