Square-heptagrammic duoprism

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Square-heptagrammic duoprism
4-7-2 duoprism.png
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymSashedip
Info
Coxeter diagramx4o x7/2o
SymmetryBC2×I2(7), order 112
ArmySemi-uniform squahedip
RegimentSashedip
Elements
Vertex figureDigonal disphenoid, 2cos(2π/7) (base 1) and 2 (base 2 and sides)
Cells7 cubes, 4 heptagrammic prisms
Faces7+28 squares, 4 heptagrams
Edges28+28
Vertices28
Measures (edge length 1)
Circumradius2+csc2(2π/7)/2 ≈ 0.95341
Hypervolume7/[4tan(2π/7)] ≈ 1.39558
Dichoral anglesCube–4–cube: 3π/7 ≈ 77.14286°
 Ship–7/2–ship: 90°
 Cube–4–ship: 90°
Central density2
Related polytopes
DualSquare-heptagrammic duotegum
ConjugatesSquare-heptagonal duoprism, Square-great heptagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame


The square-heptagrammic duoprism, also known as sashedip or the 4-7/2 duoprism, is a uniform duoprism that consists of 7 cubes and 4 heptagrammic prisms, with 2 of each meeting at each vertex.

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

Vertex coordinates[edit | edit source]

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

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

External links[edit | edit source]

Bowers, Jonathan. "Category A: Duoprisms".