# Enneagrammic-grand hendecagrammic duoprism

Enneagrammic-grand hendecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx9/2o x11/5o
SymmetryI2(9)×I2(11), order 396
ArmySemi-uniform ehendip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(2π/9) (base 1), 2cos(5π/11) (base 2), 2 (sides)
Cells11 enneagrammic prisms, 9 grand hendecagrammic prisms
Faces11 enneagrams, 9 grand hendecagrams, 99 squares
Edges99+99
Vertices99
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{1}{4\sin^2\frac{2\pi}{9}}+\frac{1}{4\sin^2\frac{5\pi}{11}}}≈0.92749}$
Hypervolume${\displaystyle \frac{99}{16\tan\frac{2\pi}{9}\tan\frac{5\pi}{11}}≈1.06022}$
Dichoral anglesStep–9/2–step: π/11 ≈ 16.36364°
11/5p–11/5–11/5p: 100°
Step–4–11/5p: 90°
Central density10
Related polytopes
DualEnneagrammic-grand hendecagrammic duotegum
ConjugatesEnneagonal-hendecagonal duoprism, Enneagonal-small hendecagrammic 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, 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 enneagrammic-grand hendecagrammic duoprism, also known as the 9/2-11/5 duoprism, is a uniform duoprism that consists of 11 enneagrammic prisms and 9 grand hendecagrammic prisms, with 2 of each meeting at each vertex.

The name can also refer to the great enneagrammic-grand hendecagrammic duoprism.

## Coordinates

The vertex coordinates of an enneagrammic-grand hendecagrammic duoprism, centered at the origin and with edge length 4sin(2π/9)sin(5π/11), are given by:

• (2sin(5π/11), 0, 2sin(2π/9), 0),
• (2sin(5π/11), 0, 2sin(2π/9)cos(2π/11), ±2sin(2π/9)sin(2π/11)),
• (2sin(5π/11), 0, 2sin(2π/9)cos(4π/11), ±2sin(2π/9)sin(4π/11)),
• (2sin(5π/11), 0, 2sin(2π/9)cos(6π/11), ±2sin(2π/9)sin(6π/11)),
• (2sin(5π/11), 0, 2sin(2π/9)cos(8π/11), ±2sin(2π/9)sin(8π/11)),
• (2sin(5π/11), 0, 2sin(2π/9)cos(10π/11), ±2sin(2π/9)sin(10π/11)),
• (2sin(5π/11)cos(2π/9), ±2sin(5π/11)sin(2π/9), 2sin(2π/9), 0),
• (2sin(5π/11)cos(2π/9), ±2sin(5π/11)sin(2π/9), 2sin(2π/9)cos(2π/11), ±2sin(2π/9)sin(2π/11)),
• (2sin(5π/11)cos(2π/9), ±2sin(5π/11)sin(2π/9), 2sin(2π/9)cos(4π/11), ±2sin(2π/9)sin(4π/11)),
• (2sin(5π/11)cos(2π/9), ±2sin(5π/11)sin(2π/9), 2sin(2π/9)cos(6π/11), ±2sin(2π/9)sin(6π/11)),
• (2sin(5π/11)cos(2π/9), ±2sin(5π/11)sin(2π/9), 2sin(2π/9)cos(8π/11), ±2sin(2π/9)sin(8π/11)),
• (2sin(5π/11)cos(2π/9), ±2sin(5π/11)sin(2π/9), 2sin(2π/9)cos(10π/11), ±2sin(2π/9)sin(10π/11)),
• (2sin(5π/11)cos(4π/9), ±2sin(5π/11)sin(4π/9), 2sin(2π/9), 0),
• (2sin(5π/11)cos(4π/9), ±2sin(5π/11)sin(4π/9), 2sin(2π/9)cos(2π/11), ±2sin(2π/9)sin(2π/11)),
• (2sin(5π/11)cos(4π/9), ±2sin(5π/11)sin(4π/9), 2sin(2π/9)cos(4π/11), ±2sin(2π/9)sin(4π/11)),
• (2sin(5π/11)cos(4π/9), ±2sin(5π/11)sin(4π/9), 2sin(2π/9)cos(6π/11), ±2sin(2π/9)sin(6π/11)),
• (2sin(5π/11)cos(4π/9), ±2sin(5π/11)sin(4π/9), 2sin(2π/9)cos(8π/11), ±2sin(2π/9)sin(8π/11)),
• (2sin(5π/11)cos(4π/9), ±2sin(5π/11)sin(4π/9), 2sin(2π/9)cos(10π/11), ±2sin(2π/9)sin(10π/11)),
• (–sin(5π/11), ±sin(5π/11)3, 2sin(2π/9), 0),
• (–sin(5π/11), ±sin(5π/11)3, 2sin(2π/9)cos(2π/11), ±2sin(2π/9)sin(2π/11)),
• (–sin(5π/11), ±sin(5π/11)3, 2sin(2π/9)cos(4π/11), ±2sin(2π/9)sin(4π/11)),
• (–sin(5π/11), ±sin(5π/11)3, 2sin(2π/9)cos(6π/11), ±2sin(2π/9)sin(6π/11)),
• (–sin(5π/11), ±sin(5π/11)3, 2sin(2π/9)cos(8π/11), ±2sin(2π/9)sin(8π/11)),
• (–sin(5π/11), ±sin(5π/11)3, 2sin(2π/9)cos(10π/11), ±2sin(2π/9)sin(10π/11)),
• (2sin(5π/11)cos(8π/9), ±2sin(5π/11)sin(8π/9), 2sin(2π/9), 0),
• (2sin(5π/11)cos(8π/9), ±2sin(5π/11)sin(8π/9), 2sin(2π/9)cos(2π/11), ±2sin(2π/9)sin(2π/11)),
• (2sin(5π/11)cos(8π/9), ±2sin(5π/11)sin(8π/9), 2sin(2π/9)cos(4π/11), ±2sin(2π/9)sin(4π/11)),
• (2sin(5π/11)cos(8π/9), ±2sin(5π/11)sin(8π/9), 2sin(2π/9)cos(6π/11), ±2sin(2π/9)sin(6π/11)),
• (2sin(5π/11)cos(8π/9), ±2sin(5π/11)sin(8π/9), 2sin(2π/9)cos(8π/11), ±2sin(2π/9)sin(8π/11)),
• (2sin(5π/11)cos(8π/9), ±2sin(5π/11)sin(8π/9), 2sin(2π/9)cos(10π/11), ±2sin(2π/9)sin(10π/11)).