Rhombidodecadodecahedral prism

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Rhombidodecadodecahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymRadiddip
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
Hypervolume
Dichoral anglesCube–4–stip:
 Cube–4–pip:
 Raded–5/2–stip: 90°
 Raded–5–pip: 90°
 Raded–4–cube: 90°
Height1
Central density3
Related polytopes
ArmySemi-uniform Tipe
RegimentRadiddip
DualMedial deltoidal hexecontahedral tegum
ConjugateRhombidodecadodecahedral prism
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[edit | edit source]

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

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

External links[edit | edit source]