# Heptagrammic-enneagrammic duoprism

(Redirected from 7/2-9/2 duoprism)
Heptagrammic-enneagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymShestedip
Info
Coxeter diagramx7/2o x9/2o
SymmetryI2(7)×I2(9), order 252
ArmySemi-uniform heendip
RegimentShestedip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(2π/7) (base 1), 2cos(2π/9) (base 2), 2 (sides)
Cells9 heptagrammic prisms, 7 enneagrammic prisms
Faces63 squares, 9 heptagrams, 7 enneagrams
Edges63+63
Vertices63
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{1}{4\sin^2\frac{2\pi}{7}}+\frac{1}{4\sin^2\frac{2\pi}{9}}}≈1.00701}$
Hypervolume${\displaystyle \frac{63}{16\tan\frac{2\pi}{7}\tan\frac{2\pi}{9}}≈3.74217}$
Dichoral anglesShip–7/2–ship: 100°
Step–9/2–step: 3π/7 ≈ 77.14286°
Ship–4–step: 90°
Central density4
Related polytopes
DualHeptagrammic-enneagrammic duotegum
ConjugatesHeptagonal-enneagonal duoprism, Heptagonal-enneagrammic duoprism, Heptagonal-great enneagrammic duoprism, Heptagrammic-enneagonal duoprism, Heptagrammic-great enneagrammic duoprism, Great heptagrammic-enneagonal duoprism, Great heptagrammic-enneagrammic duoprism, Great heptagrammic-great enneagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame

The heptagrammic-enneagrammic duoprism, also known as shestedip or the 7/2-9/2 duoprism, is a uniform duoprism that consists of 9 heptagrammic prisms and 7 enneagrammic prisms, with 2 of each meeting at each vertex.

The name can also refer to the great heptagrammic-enneagrammic duoprism, the heptagrammic-great enneagrammic duoprism, or the great heptagrammic-great enneagrammic duoprism.

## Vertex coordinates

The coordinates of a heptagrammic-enneagrammic duoprism, centered at the origin and with edge length 4sin(2π/7)sin(2π/9), are given by:

• (2sin(2π/9), 0, 2sin(2π/7), 0),
• (2sin(2π/9), 0, 2sin(2π/7)cos(2π/9), ±2sin(2π/7)sin(2π/9)),
• (2sin(2π/9), 0, 2sin(2π/7)cos(4π/9), ±2sin(2π/7)sin(4π/9)),
• (2sin(2π/9), 0, –sin(2π/7), ±sin(2π/7)3),
• (2sin(2π/9), 0, 2sin(2π/7)cos(8π/9), ±2sin(2π/7)sin(8π/9)),
• (2sin(2π/9)cos(2π/7), ±2sin(2π/9)sin(2π/7), 2sin(2π/7), 0),
• (2sin(2π/9)cos(2π/7), ±2sin(2π/9)sin(2π/7), 2sin(2π/7)cos(2π/9), ±2sin(2π/7)sin(2π/9)),
• (2sin(2π/9)cos(2π/7), ±2sin(2π/9)sin(2π/7), 2sin(2π/7)cos(4π/9), ±2sin(2π/7)sin(4π/9)),
• (2sin(2π/9)cos(2π/7), ±2sin(2π/9)sin(2π/7), –sin(2π/7), ±sin(2π/7)3),
• (2sin(2π/9)cos(2π/7), ±2sin(2π/9)sin(2π/7), 2sin(2π/7)cos(8π/9), ±2sin(2π/7)sin(8π/9)),
• (2sin(2π/9)cos(4π/7), ±2sin(2π/9)sin(4π/7), 2sin(2π/7), 0),
• (2sin(2π/9)cos(4π/7), ±2sin(2π/9)sin(4π/7), 2sin(2π/7)cos(2π/9), ±2sin(2π/7)sin(2π/9)),
• (2sin(2π/9)cos(4π/7), ±2sin(2π/9)sin(4π/7), 2sin(2π/7)cos(4π/9), ±2sin(2π/7)sin(4π/9)),
• (2sin(2π/9)cos(4π/7), ±2sin(2π/9)sin(4π/7), –sin(2π/7), ±sin(2π/7)3),
• (2sin(2π/9)cos(4π/7), ±2sin(2π/9)sin(4π/7), 2sin(2π/7)cos(8π/9), ±2sin(2π/7)sin(8π/9)),
• (2sin(2π/9)cos(6π/7), ±2sin(2π/9)sin(6π/7), 2sin(2π/7), 0),
• (2sin(2π/9)cos(6π/7), ±2sin(2π/9)sin(6π/7), 2sin(2π/7)cos(2π/9), ±2sin(2π/7)sin(2π/9)),
• (2sin(2π/9)cos(6π/7), ±2sin(2π/9)sin(6π/7), 2sin(2π/7)cos(4π/9), ±2sin(2π/7)sin(4π/9)),
• (2sin(2π/9)cos(6π/7), ±2sin(2π/9)sin(6π/7), –sin(2π/7), ±sin(2π/7)3),
• (2sin(2π/9)cos(6π/7), ±2sin(2π/9)sin(6π/7), 2sin(2π/7)cos(8π/9), ±2sin(2π/7)sin(8π/9)).