Great enneagrammic-hendecagrammic duoprism

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Great enneagrammic-hendecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx9/4o x11/3o
SymmetryI2(9)×I2(11), order 396
ArmySemi-uniform ehendip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(4π/9) (base 1), 2cos(3π/11) (base 2), 2 (sides)
Cells11 great enneagrammic prisms, 9 hendecagrammic prisms
Faces11 great enneagrams, 9 hendecagrams, 99 squares
Edges99+99
Vertices99
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesGistep–9/4–gistep: 5π/11 ≈ 81.81818°
 11/3p–11/3–11/3p: 20°
 Gistep–4–11/3p: 90°
Central density12
Related polytopes
DualGreat enneagrammic-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, Enneagrammic-grand hendecagrammic duoprism, Great enneagrammic-hendecagonal duoprism, Great enneagrammic-small hendecagrammic duoprism, Great enneagrammic-great hendecagrammic duoprism, Great enneagrammic-grand hendecagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame


The great enneagrammic-hendecagrammic duoprism, also known as the 9/4-11/3 duoprism, is a uniform duoprism that consists of 11 great enneagrammic prisms and 9 hendecagrammic prisms, with 2 of each meeting at each vertex.

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

Coordinates[edit | edit source]

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

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

External links[edit | edit source]