Enneagrammic-hendecagonal duoprism

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Enneagrammic-hendecagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx9/2o x11o
SymmetryI2(9)×I2(11), order 396
ArmySemi-uniform ehendip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(2π/9) (base 1), 2cos(π/11) (base 2), 2 (sides)
Cells11 enneagrammic prisms, 9 hendecagonal prisms
Faces99 squares, 11 enneagrams, 9 hendecagons
Edges99+99
Vertices99
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesStep–9/2–step: 9π/11 ≈ 147.27273°
 11p–11–11p: 100°
 Step–4–11p: 90°
Central density2
Related polytopes
DualEnneagrammic-hendecagonal duotegum
ConjugatesEnneagonal-hendecagonal duoprism, Enneagonal-small hendecagrammic duoprism, Enneagonal-hendecagrammic duoprism, Enneagonal-great hendecagrammic duoprism, Enneagonal-grand hendecagrammic 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 enneagrammic-hendecagonal duoprism, also known as the 9/2-11 duoprism, is a uniform duoprism that consists of 11 enneagrammic prisms and 9 hendecagonal prisms, with 2 of each meeting at each vertex.

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

Vertex coordinates[edit | edit source]

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

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

External links[edit | edit source]