# Enneagonal-hendecagrammic duoprism

(Redirected from 11/3-9 duoprism)
Enneagonal-hendecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx9o x11/3o
SymmetryI2(9)×I2(11), order 396
ArmySemi-uniform ehendip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(π/9) (base 1), 2cos(3π/11) (base 2), 2 (sides)
Cells11 enneagonal prisms, 9 hendecagrammic prisms
Faces99 squares, 11 enneagons, 9 hendecagrams
Edges99+99
Vertices99
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{1}{4\sin^2\frac{\pi}{9}}+\frac{1}{4\sin^2\frac{3\pi}{11}}}≈1.60464}$
Hypervolume${\displaystyle \frac{99}{16\tan\frac{\pi}{9}\tan\frac{3\pi}{11}}≈14.73060}$
Dichoral anglesEp–9–ep: 5π/11 ≈ 81.81818°
11/3p–11/3–11/3p: 140°
Ep–4–11/3p: 90°
Central density3
Related polytopes
DualEnneagonal-hendecagrammic duotegum
ConjugatesEnneagonal-hendecagonal duoprism, Enneagonal-small 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-hendecagrammic duoprism, also known as the 9-11/3 duoprism, is a uniform duoprism that consists of 11 enneagonal prisms and 9 hendecagrammic prisms, with 2 of each meeting at each vertex.

The name can also refer to the enneagonal-small hendecagrammic duoprism, enneagonal-great hendecagrammic duoprism, or the enneagonal-grand hendecagrammic duoprism.

## Vertex coordinates

The coordinates of a enneagonal-hendecagrammic duoprism, centered at the origin and with edge length 4sin(π/9)sin(3π/11), are given by:

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