Compound of six pentagonal prisms

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Compound of six pentagonal prisms
Rank3
TypeUniform
Notation
Bowers style acronymKred
Elements
Components6 pentagonal prisms
Faces30 squares, 12 pentagons
Edges30+60
Vertices60
Vertex figureIsosceles triangle, edge lengths (1+5)/2, 2, 2
Measures (edge length 1)
Circumradius
Volume
Dihedral angles4–4: 108°
 4–5: 90°
Central density6
Number of external pieces180
Level of complexity34
Related polytopes
ArmySemi-uniform Ti, edge lengths (pentagons), (between ditrigons)
RegimentKred
DualCompound of six pentagonal tegums
ConjugateCompound of six pentagrammic prisms
Convex coreDodecahedron
Abstract & topological properties
Flag count360
OrientableYes
Properties
SymmetryH3+, order 60
ConvexNo
NatureTame

The chirorhombidodecahedron, rhombidodecahedron, kred, or compound of six pentagonal prisms is a uniform polyhedron compound. It consists of 30 squares and 12 pentagons, with one pentagon and two squares joining at a vertex.

Its quotient prismatic equivalent is the pentagonal prismatic hexateroorthowedge, which is eight-dimensional.

Vertex coordinates[edit | edit source]

The vertices of a chirorhombidodecahedron of edge length 1 are given by all permutations of:

  • ,

Plus all even permutations of:

  • ,
  • .

Related polyhedra[edit | edit source]

This compound is chiral. The compound of the two enantiomorphs is the disrhombidodecahedron.

External links[edit | edit source]