Rank4
TypeUniform
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${\displaystyle {\sqrt {2}}\approx 1.41421}$
Hypervolume${\displaystyle 19{\sqrt {5}}\approx 42.48529}$
Dichoral anglesCube–4–stip: ${\displaystyle \arccos \left(-{\sqrt {\frac {5+{\sqrt {5}}}{10}}}\right)\approx 148.28253^{\circ }}$
Cube–4–pip: ${\displaystyle \arccos \left(-{\sqrt {\frac {5-{\sqrt {5}}}{10}}}\right)\approx 121.71747^{\circ }}$
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:

• ${\displaystyle \left(\pm {\frac {\sqrt {5}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)}$

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

• ${\displaystyle \left(0,\,\pm {\frac {3+{\sqrt {5}}}{4}},\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(\pm 1,\,\pm {\frac {{\sqrt {5}}-1}{4}},\,\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}}\right).}$