Pentagonal-dodecagonal duoprism

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Pentagonal-dodecagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymPitwadip
Info
Coxeter diagramx5o x12o
SymmetryH2×I2(12), order 240
ArmyPitwadip
RegimentPitwadip
Elements
Vertex figureDigonal disphenoid, edge lengths (1+5)/2 (base 1), (2+6)/2 (base 2), and 2 (sides)
Cells12 pentagonal prisms, 5 dodecagonal prisms
Faces60 squares, 12 pentagons, 5 dodecagons,
Edges60+60
Vertices60
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesTwip–12–twip: 108°
 Pip–5–pip: 150°
 Twip–4–pip: 90°
Central density1
Euler characteristic0
Number of pieces17
Level of complexity6
Related polytopes
DualPentagonal-dodecagonal duotegum
ConjugatesPentagonal-dodecagrammic duoprism, Pentagrammic-dodecagonal duoprism, Pentagrammic-dodecagrammic duoprism
Properties
ConvexYes
OrientableYes
NatureTame

The pentagonal-dodecagonal duoprism or pitwadip, also known as the 5-12 duoprism, is a uniform duoprism that consists of 5 dodecagonal prisms and 12 pentagonal prisms, with two of each joining at each vertex.

Vertex coordinates[edit | edit source]

The coordinates of a pentagonal-dodecagonal duoprism, centered at the origin and with unit edge length, are given by:

Representations[edit | edit source]

A pentagonal-dodecagonal duoprism has the following Coxeter diagrams:

  • x5o x12o (full symmetry)
  • x5o x6x (dodecagons as dihexagons)

External links[edit | edit source]