# Quasirhombicosidodecahedral prism

Quasirhombicosidodecahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymQriddip
Coxeter diagramx x5/3o3x ()
Elements
Cells20 triangular prisms, 30 cubes, 12 pentagrammic prisms, 2 quasirhombicosidodecahedra
Faces40 triangles, 60+60+60 squares, 24 pentagrams
Edges60+120+120
Vertices120
Vertex figureCrossed trapezoidal pyramid, edge lengths 1, 2, (5–1)/2, 2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {{\sqrt {10}}-{\sqrt {2}}}{2}}\approx 0.87403}$
Hypervolume${\displaystyle {\frac {29{\sqrt {5}}-60}{3}}\approx 1.61532}$
Dichoral anglesQrid–5/2–stip: 90°
Qrid–3–trip: 90°
Qrid–4–cube: 90°
Trip–4–cube: ${\displaystyle \arccos \left({\frac {{\sqrt {15}}-{\sqrt {3}}}{6}}\right)\approx 69.09484^{\circ }}$
Cube–4–stip: ${\displaystyle \arccos \left({\sqrt {\frac {5-{\sqrt {5}}}{10}}}\right)\approx 58.28253^{\circ }}$
Height1
Central density13
Related polytopes
ArmySemi-uniform Tipe
DualGreat deltoidal hexecontahedral tegum
ConjugateSmall rhombicosidodecahedral prism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The quasirhombicosidodecahedral prism or qriddip is a prismatic uniform polychoron that consists of 2 quasirhombicosidodecahedra, 12 pentagrammic prisms, 20 triangular prisms, and 30 cubes. Each vertex joins 1 quasirhombicosidodecahedron, 1 pentagrammic prism, 1 triangular prism, and 2 cubes. As the name suggests, it is a prism based on the quasirhombicosidodecahedron.

## Vertex coordinates

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