Heptagonal-decagonal duoprism

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Heptagonal-decagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymHedadip
Info
Coxeter diagramx7o x10o
SymmetryI2(7)×I2(10), order 280
ArmyHedadip
RegimentHedadip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(π/7) (base 1), (5+5)/2 (base 2), and 2 (sides)
Cells10 heptagonal prisms, 7 decagonal prisms
Faces70 squares, 10 heptagons, 7 decagons
Edges70+70
Vertices70
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesHep–7–hep: 144°
 Dip–10–dip:
 Hep–4–dip: 90°
Central density1
Euler characteristic0
Number of pieces17
Level of complexity6
Related polytopes
DualHeptagonal-decagonal duotegum
ConjugatesHeptagonal-decagrammic duoprism, Heptagrammic-decagonal duoprism, Heptagrammic-decagrammic duoprism, Great heptagrammic-decagonal duoprism, Great heptagrammic-decagrammic duoprism
Properties
ConvexYes
OrientableYes
NatureTame


The heptagonal-decagonal duoprism or hedadip, also known as the 7-10 duoprism, is a uniform duoprism that consists of 7 decagonal prisms and 10 heptagonal prisms, with two of each joining at each vertex.

Vertex coordinates[edit | edit source]

The coordinates of a heptagonal-decagonal duoprism, centered at the origin and with edge length 2sin(π/7), are given by:

  • (1, 0, ±sin(π/7), ±sin(π/7)5+25),
  • (1, 0, ±sin(π/7)(3+5)/2, ±sin(π/7)(5+5)/2),
  • (1, 0, ±sin(π/7)(1+5), 0),
  • (cos(2π/7), ±sin(2π/7), ±sin(π/7), ±sin(π/7)5+25),
  • (cos(2π/7), ±sin(2π/7), ±sin(π/7)(3+5)/2, ±sin(π/7)(5+5)/2),
  • (cos(2π/7), ±sin(2π/7), ±sin(π/7)(1+5), 0),
  • (cos(4π/7), ±sin(4π/7), ±sin(π/7), ±sin(π/7)5+25),
  • (cos(4π/7), ±sin(4π/7), ±sin(π/7)(3+5)/2, ±sin(π/7)(5+5)/2),
  • (cos(4π/7), ±sin(4π/7), ±sin(π/7)(1+5), 0),
  • (cos(6π/7), ±sin(6π/7), ±sin(π/7), ±sin(π/7)5+25),
  • (cos(6π/7), ±sin(6π/7), ±sin(π/7)(3+5)/2, ±sin(π/7)(5+5)/2),
  • (cos(6π/7), ±sin(6π/7), ±sin(π/7)(1+5), 0).

Representations[edit | edit source]

A heptagonal-decagonal duoprism has the following Coxeter diagrams:

  • x7o x10o (full symmetry)
  • x5x x7o (decagons as dipentagons)

External links[edit | edit source]