Enneagonal-grand hendecagrammic duoprism

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Enneagonal-grand hendecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx9o x11/5o
SymmetryI2(9)×I2(11), order 396
ArmySemi-uniform ehendip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(π/9) (base 1), 2cos(5π/11) (base 2), 2 (sides)
Cells11 enneagonal prisms, 9 grand hendecagrammic prisms
Faces99 squares, 11 enneagons, 9 grand hendecagrams
Edges99+99
Vertices99
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesEp–9–ep: π/11 ≈ 16.36364°
 11/5p–11/5–11/5p: 140°
 Ep–4–11/5p: 90°
Central density5
Related polytopes
DualEnneagonal-grand hendecagrammic duotegum
ConjugatesEnneagonal-hendecagonal duoprism, Enneagonal-small hendecagrammic duoprism, Enneagonal-hendecagrammic duoprism, Enneagonal-great 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-grand hendecagrammic duoprism, also known as the 9-11/5 duoprism, is a uniform duoprism that consists of 11 enneagonal prisms and 9 grand hendecagrammic prisms, with 2 of each meeting at each vertex.

Vertex coordinates[edit | edit source]

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

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

External links[edit | edit source]