Pentagonal-octagonal duoprism

The pentagonal-octagonal duoprism or podip, also known as the 5-8 duoprism, is a uniform duoprism that consists of 5 octagonal prisms and 8 pentagonal prisms, with two of each joining at each vertex.

Pentagonal-octagonal duoprism
Rank4
TypeUniform
Notation
Bowers style acronymPodip
Coxeter diagramx5o x8o ()
Elements
Cells8 pentagonal prisms, 5 octagonal prisms
Faces40 squares, 8 pentagons, 5 octagons
Edges40+40
Vertices40
Vertex figureDigonal disphenoid, edge lengths (1+5)/2 (base 1), 2+2 (base 2), and 2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesPip–5–pip: 135°
 Op–8–op: 108°
 Pip–4–op: 90°
Central density1
Number of external pieces13
Level of complexity6
Related polytopes
ArmyPodip
RegimentPodip
DualPentagonal-octagonal duotegum
ConjugatesPentagonal-octagrammic duoprism,
Pentagrammic-octagonal duoprism,
Pentagrammic-octagrammic duoprism
Abstract & topological properties
Flag count960
Euler characteristic0
OrientableYes
Properties
SymmetryH2×I2(8), order 160
Flag orbits6
ConvexYes
NatureTame

Gallery edit

Vertex coordinates edit

Coordinates for the vertices of a pentagonal-octagonal duoprism with edge length 1 are given by:

  •  ,
  •  ,
  •  ,
  •  ,
  •  ,
  •  .

Representations edit

A pentagonal-octagonal duoprism has the following Coxeter diagrams:

  • x5o x8o (       ) (full symmetry)
  • x4x x5o (       ) (B2×H2 symmetry, octagons as ditetragons)
  • ofx xxx8ooo&#xt (I2(8)×A1 axial)
  • ofx xxx4xxx&#xt (B2×A1 symmetry, ditetragonal axial)

External links edit