Great heptagrammic-enneagonal duoprism

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Great heptagrammic-enneagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymGishedip
Info
Coxeter diagramx7/3o x9o
SymmetryI2(7)×I2(9), order 252
ArmySemi-uniform heendip
RegimentGishedip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(3π/7) (base 1), 2cos(π/9) (base 2), 2 (sides)
Cells9 great heptagrammic prisms, 7 enneagonal prisms
Faces63 squares, 9 great heptagrams, 7 enneagons
Edges63+63
Vertices63
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesGiship–7/3–giship: 140°
 Ep–9–ep: π/7 ≈ 25.71429°
 Giship–4–ep: 90°
Central density3
Related polytopes
DualGreat heptagrammic-enneagonal duotegum
ConjugatesHeptagonal-enneagonal duoprism, Heptagonal-enneagrammic duoprism, Heptagonal-great enneagrammic duoprism, Heptagrammic-enneagonal duoprism, Heptagrammic-enneagrammic duoprism, Heptagrammic-great enneagrammic duoprism, Great heptagrammic-enneagrammic duoprism, Great heptagrammic-great enneagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame


The great heptagrammic-enneagonal duoprism, also known as gishedip or the 7/3-9 duoprism, is a uniform duoprism that consists of 9 great heptagrammic prisms and 7 enneagonal prisms, with 2 of each meeting at each vertex.

Vertex coordinates[edit | edit source]

The coordinates of a great heptagrammic-enneagonal duoprism, centered at the origin and with edge length 4sin(3π/7)sin(π/9), are given by:

  • (2sin(π/9), 0, 2sin(3π/7), 0),
  • (2sin(π/9), 0, 2sin(3π/7)cos(2π/9), ±2sin(3π/7)sin(2π/9)),
  • (2sin(π/9), 0, 2sin(3π/7)cos(4π/9), ±2sin(3π/7)sin(4π/9)),
  • (2sin(π/9), 0, –sin(3π/7), ±sin(3π/7)3),
  • (2sin(π/9), 0, 2sin(3π/7)cos(8π/9), ±2sin(3π/7)sin(8π/9)),
  • (2sin(π/9)cos(2π/7), ±2sin(π/9)sin(2π/7), 2sin(3π/7), 0),
  • (2sin(π/9)cos(2π/7), ±2sin(π/9)sin(2π/7), 2sin(3π/7)cos(2π/9), ±2sin(3π/7)sin(2π/9)),
  • (2sin(π/9)cos(2π/7), ±2sin(π/9)sin(2π/7), 2sin(3π/7)cos(4π/9), ±2sin(3π/7)sin(4π/9)),
  • (2sin(π/9)cos(2π/7), ±2sin(π/9)sin(2π/7), –sin(3π/7), ±sin(3π/7)3),
  • (2sin(π/9)cos(2π/7), ±2sin(π/9)sin(2π/7), 2sin(3π/7)cos(8π/9), ±2sin(3π/7)sin(8π/9)),
  • (2sin(π/9)cos(4π/7), ±2sin(π/9)sin(4π/7), 2sin(3π/7), 0),
  • (2sin(π/9)cos(4π/7), ±2sin(π/9)sin(4π/7), 2sin(3π/7)cos(2π/9), ±2sin(3π/7)sin(2π/9)),
  • (2sin(π/9)cos(4π/7), ±2sin(π/9)sin(4π/7), 2sin(3π/7)cos(4π/9), ±2sin(3π/7)sin(4π/9)),
  • (2sin(π/9)cos(4π/7), ±2sin(π/9)sin(4π/7), –sin(3π/7), ±sin(3π/7)3),
  • (2sin(π/9)cos(4π/7), ±2sin(π/9)sin(4π/7), 2sin(3π/7)cos(8π/9), ±2sin(3π/7)sin(8π/9)),
  • (2sin(π/9)cos(6π/7), ±2sin(π/9)sin(6π/7), 2sin(3π/7), 0),
  • (2sin(π/9)cos(6π/7), ±2sin(π/9)sin(6π/7), 2sin(3π/7)cos(2π/9), ±2sin(3π/7)sin(2π/9)),
  • (2sin(π/9)cos(6π/7), ±2sin(π/9)sin(6π/7), 2sin(3π/7)cos(4π/9), ±2sin(3π/7)sin(4π/9)),
  • (2sin(π/9)cos(6π/7), ±2sin(π/9)sin(6π/7), –sin(3π/7), ±sin(3π/7)3),
  • (2sin(π/9)cos(6π/7), ±2sin(π/9)sin(6π/7), 2sin(3π/7)cos(8π/9), ±2sin(3π/7)sin(8π/9)).

External links[edit | edit source]