# Compound of twelve pentagonal prisms

(Redirected from Disrhombidodecahedron)
Compound of twelve pentagonal prisms
Rank3
TypeUniform
Notation
Bowers style acronymDird
Elements
Components12 pentagonal prisms
Faces60 squares, 24 pentagons
Edges60+120
Vertices60
Vertex figureCompound of two isosceles triangles, edge lengths (1+5)/2, 2, 2
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {15+2{\sqrt {5}}}{20}}}\approx 0.98672}$
Volume${\displaystyle 3{\sqrt {25+10{\sqrt {5}}}}\approx 20.64573}$
Dihedral angles4–4: 108°
4–5: 90°
Central density12
Number of external pieces540
Level of complexity32
Related polytopes
ArmySemi-uniform Ti, edge lengths ${\displaystyle {\sqrt {\frac {5-2{\sqrt {5}}}{5}}}}$ (pentagons), ${\displaystyle {\sqrt {\frac {5-{\sqrt {5}}}{10}}}}$ (between ditrigons)
RegimentDird
DualCompound of twelve pentagonal tegums
ConjugateCompound of twelve pentagrammic prisms
Convex coreDodecahedron
Abstract & topological properties
Flag count720
OrientableYes
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The disrhombidodecahedron, dird, or compound of twelve pentagonal prisms is a uniform polyhedron compound. It consists of 60 squares and 24 pentagons, with two pentagons and four squares joining at a vertex.

It can be formed by combining the two chiral forms of the chirorhombidodecahedron, which results in vertices pairing up and two components joining per vertex.

Its quotient prismatic equivalent is the pentagonal prismatic dodecadakoorthowedge, which is fourteen-dimensional.

## Vertex coordinates

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

• ${\displaystyle \left(\pm {\sqrt {\frac {5-2{\sqrt {5}}}{20}}},\,\pm {\sqrt {\frac {5+2{\sqrt {5}}}{20}}},\,\pm {\sqrt {\frac {5+2{\sqrt {5}}}{20}}}\right)}$,

Plus all even permutations of:

• ${\displaystyle \left(0,\,\pm {\sqrt {\frac {5-{\sqrt {5}}}{40}}},\,\pm {\sqrt {\frac {5+{\sqrt {5}}}{8}}}\right)}$,
• ${\displaystyle \left(\pm {\sqrt {\frac {5-{\sqrt {5}}}{40}}},\,\pm {\sqrt {\frac {5+{\sqrt {5}}}{40}}},\,\pm {\sqrt {\frac {5+{\sqrt {5}}}{10}}}\right)}$.