Rhombicosahedral prism

Rhombicosahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymRipe
Elements
Cells30 cubes, 20 hexagonal prisms, 2 rhombicosahedra
Faces60+60+60 squares, 40 hexagons
Edges60+120+120
Vertices120
Vertex figureButterfly pyramid, edge lengths 2, 3, 2, 3 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {2}}\approx 1.41421}$
Dichoral anglesCube–4–hip #1: ${\displaystyle \arccos \left({\frac {{\sqrt {3}}-{\sqrt {15}}}{6}}\right)\approx 110.90516^{\circ }}$
Ri–4–cube: 90°
Ri–6–hip: 90°
Cube–4–hip #2: ${\displaystyle \arccos \left({\frac {{\sqrt {3}}+{\sqrt {15}}}{6}}\right)\approx 20.90516^{\circ }}$
Height1
Related polytopes
ArmySemi-uniform Tipe
DualRhombicosacronic tegum
ConjugateRhombicosahedral pirsm
Abstract & topological properties
Euler characteristic–12
OrientableNo
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The rhombicosahedral prism or ripe is a prismatic uniform polychoron that consists of 2 rhombicosahedra, 30 cubes, and 20 hexagonal prisms. Each vertex joins 1 rhombicosahedron, 2 cubes, and 2 hexagonal prisms. As the name suggests, it is a prism based on the rhombicosahedron.

Vertex coordinates

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