Great heptagrammic-decagonal duoprism


The great heptagrammic-decagonal duoprism, also known as gishdedip or the 7/3-10 duoprism, is a uniform duoprism that consists of 10 great heptagrammic prisms and 7 decagonal prisms, with 2 of each meeting at each vertex.

Great heptagrammic-decagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymGishdedip
Info
Coxeter diagramx7/3o x10o
SymmetryI2(7)×I2(10), order 280
ArmySemi-uniform hedadip
RegimentGishdedip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(3π/7) (base 1), (5+5)/2 (base 2), 2 (sides)
Cells10 great heptagrammic prisms, 7 decagonal prisms
Faces70 squares, 10 great heptagrams, 7 decagons
Edges70+70
Vertices70
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesGiship–7/3–giship: 144°
 Dip–10–dip: π/7 ≈ 25.71429°
 Giship–4–dip: 90°
Central density3
Related polytopes
DualGreat heptagrammic-decagonal duotegum
ConjugatesHeptagonal-decagonal duoprism, Heptagonal-decagrammic duoprism, Heptagrammic-decagonal duoprism, Heptagrammic-decagrammic duoprism, Great heptagrammic-decagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame

Vertex coordinatesEdit

The coordinates of a great heptagrammic-decagonal duoprism, centered at the origin and with edge length 2sin(3π/7), are given by:

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

External linksEdit