Rank4
TypeUniform
SpaceSpherical
Notation
Coxeter diagramx x5/2o5x ()
Elements
Cells30 cubes, 12 pentagonal prisms, 12 pentagrammic prisms, 2 rhombidodecadodecahedra
Faces60+60+60 squares, 24 pentagons, 24 pentagrams
Edges60+120+120
Vertices120
Vertex figureIsosceles trapezoidal pyramid, edge lengths (5–1)/2, 2, (1+5)/2, 2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle \sqrt2 ≈ 1.41421}$
Hypervolume${\displaystyle 19\sqrt5 ≈ 42.48529}$
Dichoral anglesCube–4–stip: ${\displaystyle \arccos\left(-\sqrt{\frac{5+\sqrt5}{10}}\right) ≈ 148.28253°}$
Cube–4–pip: ${\displaystyle \arccos\left(-\sqrt{\frac{5-\sqrt5}{10}}\right) ≈ 121.71747°}$
Height1
Central density3
Related polytopes
ArmySemi-uniform Tipe
DualMedial deltoidal hexecontahedral tegum
Abstract & topological properties
Euler characteristic–8
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The rhombidodecadodecahedral prism or radiddip is a prismatic uniform polychoron that consists of 2 rhombidodecadodecahedra, 12 pentagonal prisms, 12 pentagrammic prisms, and 30 cubes. Each vertex joins 1 rhombidodecadodecahedron, 1 pentagonal prism, 1 pentagrammic prism, and 2 cubes. As the name suggests, it is a prism based on the rhombidodecadodecahedron.

The rhombidodecadodecahedral prism can be vertex-inscribed into the ditetrahedronary dishecatonicosachoron.

## Vertex coordinates

The vertices of a rhombidodecadodecahedral prism of edge length 1 are given by all permutations of the first three coordinates of:

• ${\displaystyle \left(±\frac{\sqrt5}{2},\,±\frac12,\,±\frac12,\,±\frac12\right)}$

along with all even permutations of the first three coordinates of:

• ${\displaystyle \left(0,\,±\frac{3+\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac12\right),}$
• ${\displaystyle \left(±1,\,±\frac{\sqrt5-1}{4},\,±\frac{1+\sqrt5}{4},\,±\frac12\right).}$