# Heptagonal-enneagonal duoprism

(Redirected from 7-9 duoprism)
Heptagonal-enneagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymHeendip
Info
Coxeter diagramx7o x9o
SymmetryI2(7)×I2(9), order 252
ArmyHeendip
RegimentHeendip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(π/7) (base 1), 2cos(π/9) (base 2), and 2 (sides)
Cells9 heptagonal prisms, 7 enneagonal prisms
Faces63 squares, 9 heptagons, 7 enneagons
Edges63+63
Vertices63
Measures (edge length 1)
Circumradius$\sqrt{\frac{1}{4\sin^2\frac\pi7}+\frac{1}{4\sin^2\frac\pi9}} ≈ 1.86149$ Hypervolume$\frac{63}{16\tan\frac\pi7\tan\frac\pi9} ≈ 22.46421$ Dichoral anglesHep–7–hep: 140°
Ep–9–ep: $\frac{5\pi}{7} ≈ 128.57143°$ Hep–4–ep: 90°
Central density1
Euler characteristic0
Number of pieces16
Level of complexity6
Related polytopes
DualHeptagonal-enneagonal duotegum
ConjugatesHeptagonal-enneagrammic duoprism, Heptagonal-great enneagrammic duoprism, Heptagrammic-enneagonal duoprism, Heptagrammic-enneagrammic duoprism, Heptagrammic-great enneagrammic duoprism, Great heptagrammic-enneagonal duoprism, Great heptagrammic-enneagrammic duoprism, Great heptagrammic-great enneagrammic duoprism
Properties
ConvexYes
OrientableYes
NatureTame

The heptagonal-enneagonal duoprism or heendip, also known as the 7-9 duoprism, is a uniform duoprism that consists of 7 enneagonal prisms and 9 heptagonal prisms, with two of each joining at each vertex.

## Vertex coordinates

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

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