Quasirhombicosidodecahedron

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Quasirhombicosidodecahedron
Rank3
TypeUniform
Notation
Bowers style acronymQrid
Coxeter diagramx5/3o3x ()
Elements
Faces20 triangles, 30 squares, 12 pentagrams
Edges60+60
Vertices60
Vertex figureCrossed isosceles trapezoid, edge lengths 1, 2, (5–1)/2, 2
Measures (edge length 1)
Circumradius
Volume
Dihedral angles4–3:
 5/2–4:
Central density13
Number of external pieces980
Level of complexity59
Related polytopes
ArmySemi-uniform Ti, edge lengths (pentagons), (between ditrigons)
RegimentGaddid
DualGreat deltoidal hexecontahedron
ConjugateSmall rhombicosidodecahedron
Convex coreRhombic triacontahedron
Abstract & topological properties
Flag count480
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The quasirhombicosidodecahedron, also commonly known as simply the nonconvex great rhombicosidodecahedron, or qrid is a uniform polyhedron. It consists of 20 triangles, 30 squares, and 12 pentagrams, with one triangle, two squares, and one pentagram meeting at each vertex. It can be obtained by quasicantellation of the great stellated dodecahedron or great icosahedron, or equivalently by pushing either polyhedron's faces inward and filling the gaps with appropriate faces.

It is also sometimes called a great rhombicosidodecahedron, but is not to be confused with the convex polyhedron with the same name.

It is a faceting of the great dodecicosidodecahedron, using the original's 12 pentagrams and 20 triangles along with 30 additional squares.

Vertex coordinates[edit | edit source]

Its vertices are the same as those of its regiment colonel, the great dodecicosidodecahedron.

External links[edit | edit source]