# Square-heptagrammic duoprism

(Redirected from 7/2-4 duoprism)
Square-heptagrammic duoprism
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)
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

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)).