Pentagonal-decagonal duoprism

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Pentagonal-decagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymPadedip
Info
Coxeter diagramx5o x10o
SymmetryH2×I2(10), order 200
ArmyPadedip
RegimentPadedip
Elements
Vertex figureDigonal disphenoid, edge lengths (1+5)/2 (base 1), (5+5)/2 (base 2), and 2 (sides)
Cells10 pentagonal prisms, 5 decagonal prisms
Faces50 squares, 10 pentagons, 5 decagons
Edges50+50
Vertices50
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesPip–5–pip: 144°
 Dip–5–dip: 108°
 Dip–4–pip: 90°
Central density1
Euler characteristic0
Number of pieces15
Level of complexity6
Related polytopes
DualPentagonal-decagonal duotegum
ConjugatesPentagonal-decagrammic duoprism, Pentagrammic-decagonal duoprism, Pentagrammic-decagrammic duoprism
Properties
ConvexYes
OrientableYes
NatureTame


The pentagonal-decagonal duoprism or padedip, also known as the 5-10 duoprism, is a uniform duoprism that consists of 5 decagonal prisms and 10 pentagonal prisms, with two of each joining at each vertex.

The convex hull of two orthogonal pentagonal-decagonal duoprisms is either the pentagonal duoexpandoprism or the pentagonal duotruncatoprism.

Vertex coordinates[edit | edit source]

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

Representations[edit | edit source]

A pentagonal-decagonal duoprism has the following Coxeter diagrams:

  • x5o x10o (full symmetry)
  • x5x x5o (edcagons as dipentagons, pentagon duoprism symmetry)
  • ofx xxx10ooo&#xt (decagonal axial)
  • ofx xxx5xxx&#xt (dipentagonal axial symmetry)

External links[edit | edit source]