Pentagonal-icosidodecahedral duoprism

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Pentagonal-icosidodecahedral duoprism
Rank5
TypeUniform
Notation
Bowers style acronymPid
Coxeter diagramx5o o5x3o ()
Elements
Tera20 triangular-pentagonal duoprisms, 12 pentagonal duoprisms, 5 icosidodecahedral prisms
Cells100 triangular prisms, 60+60 pentagonal prisms, 5 icosidodecahedra
Faces100 triangles, 300 squares, 30+60 pentagons
Edges150+300
Vertices150
Vertex figureRectangular scalene, edge lengths 1, (1+5)/2, 1, (1+5)/2 (base rectangle), (1+5)/2 (top), 2 (side edges)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesTrapedip–pip–pedip:
 Iddip–id–iddip: 108°
 Trapedip–trip–iddip: 90°
 Pedip–pip–iddip: 90°
Central density1
Number of external pieces37
Level of complexity20
Related polytopes
ArmyPid
RegimentPid
DualPentagonal-rhombic triacontahedral duotegum
ConjugatePentagrammic-great icosidodecahedral duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryH3×H2, order 1200
ConvexYes
NatureTame

The pentagonal-icosidodecahedral duoprism or pid is a convex uniform duoprism that consists of 5 icosidodecahedral prisms, 12 pentagonal duoprisms, and 20 triangular-pentagonal duoprisms. Each vertex joins 2 icosidodecahedral prisms, 2 triangular-pentagonal duoprisms, and 2 pentagonal duoprisms.

Vertex coordinates[edit | edit source]

The vertices of a pentagonal-icosidodecahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of:

as well as all even permutations of the last three coordinates of:

External links[edit | edit source]

  • Klitzing, Richard. "pid".