# Quasirhombicosidodecahedral prism

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.

Quasirhombicosidodecahedral prism
Rank4
TypeUniform
SpaceSpherical
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${\displaystyle \frac{\sqrt{10}-\sqrt2}{2} ≈ 0.87403}$
Hypervolume${\displaystyle \frac{29\sqrt5-60}{3} ≈ 1.61532}$
Dichoral anglesQrid–5/2–stip: 90°
Qrid–3–trip: 90°
Qrid–4–cube: 90°
Trip–4–cube: ${\displaystyle \arccos\left(\frac{\sqrt{15}-\sqrt3}{6}\right) ≈ 69.09484°}$
Cube–4–stip: ${\displaystyle \arccos\left(\sqrt{\frac{5-\sqrt5}{10}}\right) ≈ 58.28253°}$
Height1
Central density13
Related polytopes
ArmySemi-uniform Tipe
DualGreat deltoidal hexecontahedral tegum
ConjugateSmall rhombicosidodecahedral prism
Abstract properties
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame
Discovered by{{{discoverer}}}

## Vertex coordinates

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