Small hendecagrammic-hendecagrammic duoprism

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Small hendecagrammic-hendecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx11/2o x11/3o
SymmetryI2(11)×I2(11), order 484
ArmySemi-uniform handip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(2π/11) (base 1), 2cos(3π/11) (base 2), 2 (sides)
Cells11 small hendecagrammic prisms, 11 hendecagrammic prisms
Faces11 small hendecagrams, 11 hendecagrams, 121 squares
Edges121+121
Vertices121
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles11/2p–11/2–11/2p: 5π/11 ≈ 81.81818°
 11/3p–11/3–11/3p: 7π/11 ≈ 114.54545°
 11/2p–4–11/3p: 90°
Central density6
Related polytopes
DualSmall hendecagrammic-hendecagrammic duotegum
ConjugatesHendecagonal-small hendecagrammic duoprism, Hendecagonal-hendecagrammic duoprism, Hendecagonal-great hendecagrammic duoprism, Hendecagonal-grand hendecagrammic duoprism, Small hendecagrammic-great hendecagrammic duoprism, Small hendecagrammic-grand hendecagrammic duoprism, Hendecagrammic-great hendecagrammic duoprism, Hendecagrammic-grand hendecagrammic duoprism, Great hendecagrammic-grand hendecagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame


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

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

Coordinates[edit | edit source]

The vertex coordinates of a small hendecagrammic-hendecagrammic duoprism, centered at the origin and with edge length 4sin(2π/11)sin(3π/11), are given by:

  • (2sin(3π/11), 0, 2sin(2π/11), 0),
  • (2sin(3π/11), 0, sin(4π/11), ±2sin2(2π/11)),
  • (2sin(3π/11), 0, 2sin(2π/11)cos(4π/11), ±2sin(2π/11)sin(4π/11)),
  • (2sin(3π/11), 0, 2sin(2π/11)cos(6π/11), ±2sin(2π/11)sin(6π/11)),
  • (2sin(3π/11), 0, 2sin(2π/11)cos(8π/11), ±2sin(2π/11)sin(8π/11)),
  • (2sin(3π/11), 0, 2sin(2π/11)cos(10π/11), ±2sin(2π/11)sin(10π/11)),
  • (2sin(3π/11)cos(2π/11), ±2sin(3π/11)sin(2π/11), 2sin(2π/11), 0),
  • (2sin(3π/11)cos(2π/11), ±2sin(3π/11)sin(2π/11), sin(4π/11), ±2sin2(2π/11)),
  • (2sin(3π/11)cos(2π/11), ±2sin(3π/11)sin(2π/11), 2sin(2π/11)cos(4π/11), ±2sin(2π/11)sin(4π/11)),
  • (2sin(3π/11)cos(2π/11), ±2sin(3π/11)sin(2π/11), 2sin(2π/11)cos(6π/11), ±2sin(2π/11)sin(6π/11)),
  • (2sin(3π/11)cos(2π/11), ±2sin(3π/11)sin(2π/11), 2sin(2π/11)cos(8π/11), ±2sin(2π/11)sin(8π/11)),
  • (2sin(3π/11)cos(2π/11), ±2sin(3π/11)sin(2π/11), 2sin(2π/11)cos(10π/11), ±2sin(2π/11)sin(10π/11)),
  • (2sin(3π/11)cos(4π/11), ±2sin(3π/11)sin(4π/11), 2sin(2π/11), 0),
  • (2sin(3π/11)cos(4π/11), ±2sin(3π/11)sin(4π/11), sin(4π/11), ±2sin2(2π/11)),
  • (2sin(3π/11)cos(4π/11), ±2sin(3π/11)sin(4π/11), 2sin(2π/11)cos(4π/11), ±2sin(2π/11)sin(4π/11)),
  • (2sin(3π/11)cos(4π/11), ±2sin(3π/11)sin(4π/11), 2sin(2π/11)cos(6π/11), ±2sin(2π/11)sin(6π/11)),
  • (2sin(3π/11)cos(4π/11), ±2sin(3π/11)sin(4π/11), 2sin(2π/11)cos(8π/11), ±2sin(2π/11)sin(8π/11)),
  • (2sin(3π/11)cos(4π/11), ±2sin(3π/11)sin(4π/11), 2sin(2π/11)cos(10π/11), ±2sin(2π/11)sin(10π/11)),
  • (2sin(3π/11)cos(6π/11), ±2sin(3π/11)sin(6π/11), 2sin(2π/11), 0),
  • (2sin(3π/11)cos(6π/11), ±2sin(3π/11)sin(6π/11), sin(4π/11), ±2sin2(2π/11)),
  • (2sin(3π/11)cos(6π/11), ±2sin(3π/11)sin(6π/11), 2sin(2π/11)cos(4π/11), ±2sin(2π/11)sin(4π/11)),
  • (2sin(3π/11)cos(6π/11), ±2sin(3π/11)sin(6π/11), 2sin(2π/11)cos(6π/11), ±2sin(2π/11)sin(6π/11)),
  • (2sin(3π/11)cos(6π/11), ±2sin(3π/11)sin(6π/11), 2sin(2π/11)cos(8π/11), ±2sin(2π/11)sin(8π/11)),
  • (2sin(3π/11)cos(6π/11), ±2sin(3π/11)sin(6π/11), 2sin(2π/11)cos(10π/11), ±2sin(2π/11)sin(10π/11)),
  • (2sin(3π/11)cos(8π/11), ±2sin(3π/11)sin(8π/11), 2sin(2π/11), 0),
  • (2sin(3π/11)cos(8π/11), ±2sin(3π/11)sin(8π/11), sin(4π/11), ±2sin2(2π/11)),
  • (2sin(3π/11)cos(8π/11), ±2sin(3π/11)sin(8π/11), 2sin(2π/11)cos(4π/11), ±2sin(2π/11)sin(4π/11)),
  • (2sin(3π/11)cos(8π/11), ±2sin(3π/11)sin(8π/11), 2sin(2π/11)cos(6π/11), ±2sin(2π/11)sin(6π/11)),
  • (2sin(3π/11)cos(8π/11), ±2sin(3π/11)sin(8π/11), 2sin(2π/11)cos(8π/11), ±2sin(2π/11)sin(8π/11)),
  • (2sin(3π/11)cos(8π/11), ±2sin(3π/11)sin(8π/11), 2sin(2π/11)cos(10π/11), ±2sin(2π/11)sin(10π/11)),
  • (2sin(3π/11)cos(10π/11), ±2sin(3π/11)sin(10π/11), 2sin(2π/11), 0),
  • (2sin(3π/11)cos(10π/11), ±2sin(3π/11)sin(10π/11), sin(4π/11), ±2sin2(2π/11)),
  • (2sin(3π/11)cos(10π/11), ±2sin(3π/11)sin(10π/11), 2sin(2π/11)cos(4π/11), ±2sin(2π/11)sin(4π/11)),
  • (2sin(3π/11)cos(10π/11), ±2sin(3π/11)sin(10π/11), 2sin(2π/11)cos(6π/11), ±2sin(2π/11)sin(6π/11)),
  • (2sin(3π/11)cos(10π/11), ±2sin(3π/11)sin(10π/11), 2sin(2π/11)cos(8π/11), ±2sin(2π/11)sin(8π/11)),
  • (2sin(3π/11)cos(10π/11), ±2sin(3π/11)sin(10π/11), 2sin(2π/11)cos(10π/11), ±2sin(2π/11)sin(10π/11)).

External links[edit | edit source]