Heptagrammic-octagrammic duoprism

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(Redirected from 7/2-8/3 duoprism)
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Heptagrammic-octagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymShestodip
Info
Coxeter diagramx7/2o x8/3o
SymmetryI2(7)×I2(8), order 224
ArmySemi-uniform heodip
RegimentShestodip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(2π/7) (base 1), 2–2 (base 2), 2 (sides)
Cells8 heptagrammic prisms, 7 octagrammic prisms
Faces56 squares, 8 heptagrams, 7 octagrams
Edges56+56
Vertices56
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesShip–7/2–ship: 45°
 Stop–8/3–stop: 3π/7 ≈ 77.14286°
 Ship–4–stop: 90°
Central density6
Related polytopes
DualHeptagrammic-octagrammic duotegum
ConjugatesHeptagonal-octagonal duoprism, Heptagonal-octagrammic duoprism, Heptagrammic-octagonal duoprism, Great heptagrammic-octagonal duoprism, Great heptagrammic-octagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame


The heptagrammic-octagrammic duoprism, also known as shestodip or the 7/2-8/3 duoprism, is a uniform duoprism that consists of 8 heptagrammic prisms and 7 octagrammic prisms, with 2 of each meeting at each vertex.

The name can also refer to the great heptagrammic-octagrammic duoprism.

Vertex coordinates[edit | edit source]

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

  • (1, 0, ±sin(2π/7)(2–1), ±sin(2π/7)),
  • (1, 0, ±sin(2π/7), ±sin(2π/7)(2–1)),
  • (cos(2π/7), ±sin(2π/7), ±sin(2π/7)(2–1), ±sin(2π/7)),
  • (cos(2π/7), ±sin(2π/7), ±sin(2π/7), ±sin(2π/7)(2–1)),
  • (cos(4π/7), ±sin(4π/7), ±sin(2π/7)(2–1), ±sin(2π/7)),
  • (cos(4π/7), ±sin(4π/7), ±sin(2π/7), ±sin(2π/7)(2–1)),
  • (cos(6π/7), ±sin(6π/7), ±sin(2π/7)(2–1), ±sin(2π/7)),
  • (cos(6π/7), ±sin(6π/7), ±sin(2π/7), ±sin(2π/7)(2–1)).

External links[edit | edit source]