# Heptagrammic-octagrammic duoprism

(Redirected from 7/2-8/3 duoprism)
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${\displaystyle \sqrt{\frac{1}{4\sin^2\frac{2\pi}{7}}+\frac{2-\sqrt{2}}{2}}≈0.83779}$
Hypervolume${\displaystyle \frac{7(\sqrt{2}-1)}{2\tan\frac{2\pi}{7}}≈1.15614}$
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

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)).