Hexagonal-decagonal duoprism

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Hexagonal-decagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymHadedip
Info
Coxeter diagramx6o x10o
SymmetryG2×I2(10), order 240
ArmyHadedip
RegimentHadedip
Elements
Vertex figureDigonal disphenoid, edge lengths 3 (base 1), (5+5)/2 (base 2), and 2 (sides)
Cells10 hexagonal prisms, 6 decagonal prisms
Faces60 squares, 10 hexagons, 6 decagons
Edges60+60
Vertices60
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesHip–6–hip: 144°
 Dip–10–dip: 120°
 Dip–4–hip: 90°
Central density1
Euler characteristic0
Number of pieces16
Level of complexity6
Related polytopes
DualHexagonal-decagonal duotegum
ConjugateHexagonal-decagrammic duoprism
Properties
ConvexYes
OrientableYes
NatureTame


The hexagonal-decagonal duoprism or hadedip, also known as the 6-10 duoprism, is a uniform duoprism that consists of 6 decagonal prisms and 10 hexagonal prisms, with two of each joining at each vertex.

This polychoron can be alternated into a triangular-pentagonal duoantiprism, although it cannot be made uniform.

Vertex coordinates[edit | edit source]

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

Representations[edit | edit source]

A hexagonal-decagonal duoprism has the following Coxeter diagrams:

  • x6o x10o (full symmetry)
  • x3x x10o (hexagons as ditrigons)
  • x5x x6o (decagons as dipentagons)
  • x3x x5x (both applied)
  • xux xxx10ooo&#xt (decagonal axial)
  • xux xxx5xxx&#xt (dipentagonal axial)

External links[edit | edit source]