# Enneagonal-small hendecagrammic duoprism

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Enneagonal-small hendecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx9o x11/2o
SymmetryI2(9)×I2(11), order 396
ArmySemi-uniform ehendip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(π/9) (base 1), 2cos(2π/11) (base 2), 2 (sides)
Cells11 enneagonal prisms, 9 small hendecagrammic prisms
Faces99 squares, 11 enneagons, 9 small hendecagrams
Edges99+99
Vertices99
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{1}{4\sin^2\frac{\pi}{9}}+\frac{1}{4\sin^2\frac{2\pi}{11}}}≈1.72987}$
Hypervolume${\displaystyle \frac{99}{16\tan\frac{\pi}{9}\tan\frac{2\pi}{11}}≈26.45254}$
Dichoral anglesEp–9–ep: 7π/11 ≈ 114.54545°
11/2p–11/2–11/2p: 140°
Ep–4–11/2p: 90°
Central density2
Related polytopes
DualEnneagonal-small hendecagrammic duotegum
ConjugatesEnneagonal-hendecagonal duoprism, Enneagonal-hendecagrammic duoprism, Enneagonal-great hendecagrammic duoprism, Enneagonal-grand hendecagrammic duoprism, Enneagrammic-hendecagonal duoprism, Enneagrammic-small hendecagrammic duoprism, Enneagrammic-hendecagrammic duoprism, Enneagrammic-great hendecagrammic duoprism, Enneagrammic-grand hendecagrammic duoprism, Great enneagrammic-hendecagonal duoprism, Great enneagrammic-small hendecagrammic duoprism, Great enneagrammic-hendecagrammic duoprism, Great enneagrammic-great hendecagrammic duoprism, Great enneagrammic-grand hendecagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame

The enneagonal-small hendecagrammic duoprism, also known as the 9-11/2 duoprism, is a uniform duoprism that consists of 11 enneagonal prisms and 9 small hendecagrammic prisms, with 2 of each meeting at each vertex.

## Vertex coordinates

The coordinates of a enneagonal-small hendecagrammic duoprism, centered at the origin and with edge length 4sin(π/9)sin(2π/11), are given by:

• (2sin(2π/11), 0, 2sin(π/9), 0),
• (2sin(2π/11), 0, 2sin(π/9)cos(2π/11), ±2sin(π/9)sin(2π/11)),
• (2sin(2π/11), 0, 2sin(π/9)cos(4π/11), ±2sin(π/9)sin(4π/11)),
• (2sin(2π/11), 0, 2sin(π/9)cos(6π/11), ±2sin(π/9)sin(6π/11)),
• (2sin(2π/11), 0, 2sin(π/9)cos(8π/11), ±2sin(π/9)sin(8π/11)),
• (2sin(2π/11), 0, 2sin(π/9)cos(10π/11), ±2sin(π/9)sin(10π/11)),
• (2sin(2π/11)cos(2π/9), ±2sin(2π/11)sin(2π/9), 2sin(π/9), 0),
• (2sin(2π/11)cos(2π/9), ±2sin(2π/11)sin(2π/9), 2sin(π/9)cos(2π/11), ±2sin(π/9)sin(2π/11)),
• (2sin(2π/11)cos(2π/9), ±2sin(2π/11)sin(2π/9), 2sin(π/9)cos(4π/11), ±2sin(π/9)sin(4π/11)),
• (2sin(2π/11)cos(2π/9), ±2sin(2π/11)sin(2π/9), 2sin(π/9)cos(6π/11), ±2sin(π/9)sin(6π/11)),
• (2sin(2π/11)cos(2π/9), ±2sin(2π/11)sin(2π/9), 2sin(π/9)cos(8π/11), ±2sin(π/9)sin(8π/11)),
• (2sin(2π/11)cos(2π/9), ±2sin(2π/11)sin(2π/9), 2sin(π/9)cos(10π/11), ±2sin(π/9)sin(10π/11)),
• (2sin(2π/11)cos(4π/9), ±2sin(2π/11)sin(4π/9), 2sin(π/9), 0),
• (2sin(2π/11)cos(4π/9), ±2sin(2π/11)sin(4π/9), 2sin(π/9)cos(2π/11), ±2sin(π/9)sin(2π/11)),
• (2sin(2π/11)cos(4π/9), ±2sin(2π/11)sin(4π/9), 2sin(π/9)cos(4π/11), ±2sin(π/9)sin(4π/11)),
• (2sin(2π/11)cos(4π/9), ±2sin(2π/11)sin(4π/9), 2sin(π/9)cos(6π/11), ±2sin(π/9)sin(6π/11)),
• (2sin(2π/11)cos(4π/9), ±2sin(2π/11)sin(4π/9), 2sin(π/9)cos(8π/11), ±2sin(π/9)sin(8π/11)),
• (2sin(2π/11)cos(4π/9), ±2sin(2π/11)sin(4π/9), 2sin(π/9)cos(10π/11), ±2sin(π/9)sin(10π/11)),
• (–sin(2π/11), ±sin(2π/11)3, 2sin(π/9), 0),
• (–sin(2π/11), ±sin(2π/11)3, 2sin(π/9)cos(2π/11), ±2sin(π/9)sin(2π/11)),
• (–sin(2π/11), ±sin(2π/11)3, 2sin(π/9)cos(4π/11), ±2sin(π/9)sin(4π/11)),
• (–sin(2π/11), ±sin(2π/11)3, 2sin(π/9)cos(6π/11), ±2sin(π/9)sin(6π/11)),
• (–sin(2π/11), ±sin(2π/11)3, 2sin(π/9)cos(8π/11), ±2sin(π/9)sin(8π/11)),
• (–sin(2π/11), ±sin(2π/11)3, 2sin(π/9)cos(10π/11), ±2sin(π/9)sin(10π/11)),
• (2sin(2π/11)cos(8π/9), ±2sin(2π/11)sin(8π/9), 2sin(π/9), 0),
• (2sin(2π/11)cos(8π/9), ±2sin(2π/11)sin(8π/9), 2sin(π/9)cos(2π/11), ±2sin(π/9)sin(2π/11)),
• (2sin(2π/11)cos(8π/9), ±2sin(2π/11)sin(8π/9), 2sin(π/9)cos(4π/11), ±2sin(π/9)sin(4π/11)),
• (2sin(2π/11)cos(8π/9), ±2sin(2π/11)sin(8π/9), 2sin(π/9)cos(6π/11), ±2sin(π/9)sin(6π/11)),
• (2sin(2π/11)cos(8π/9), ±2sin(2π/11)sin(8π/9), 2sin(π/9)cos(8π/11), ±2sin(π/9)sin(8π/11)),
• (2sin(2π/11)cos(8π/9), ±2sin(2π/11)sin(8π/9), 2sin(π/9)cos(10π/11), ±2sin(π/9)sin(10π/11)).