Hendecagrammic duoprism

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Hendecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx11/3o x11/3o
SymmetryI2(11)≀S2, order 968
ArmyHandip
Elements
Vertex figureTetragonal disphenoid, edge lengths 2cos(3π/11) (bases) and 2 (sides)
Cells22 hendecagrammic prisms
Faces22 hendecagrams, 121 squares
Edges242
Vertices121
Measures (edge length 1)
Circumradius2/(2sin(3π/11)) ≈ 0.93564
Inradius1/(2tan(3π/11)) ≈ 0.43325
Hypervolume121/(16tan2(3π/11)) ≈ 5.67816
Dichoral angles11/3p–11/3–11/3p: 5π/11 ≈ 81.81818°
 11/3p–4–11/3p: 90°
Related polytopes
DualHendecagrammic duotegum
ConjugatesHendecagonal duoprism, Small hendecagrammic duoprism, Great hendecagrammic duoprism, Grand hendecagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame

The hendecagrammic duoprism, also known as the hendecagrammic-hendecagrammic duoprism, the 11/3 duoprism or the 11/3-11/3 duoprism, is a noble uniform duoprism that consists of 22 hendecagrammic prisms and 121 vertices.

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

Vertex coordinates[edit | edit source]

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

  • (1, 0, 1, 0),
  • (1, 0, cos(2π/11), ±sin(2π/11)),
  • (1, 0, cos(4π/11), ±sin(4π/11)),
  • (1, 0, cos(6π/11), ±sin(6π/11)),
  • (1, 0, cos(8π/11), ±sin(8π/11)),
  • (1, 0, cos(10π/11), ±sin(10π/11)),
  • (cos(2π/11), ±sin(2π/11), 1, 0),
  • (cos(2π/11), ±sin(2π/11), cos(2π/11), ±sin(2π/11)),
  • (cos(2π/11), ±sin(2π/11), cos(4π/11), ±sin(4π/11)),
  • (cos(2π/11), ±sin(2π/11), cos(6π/11), ±sin(6π/11)),
  • (cos(2π/11), ±sin(2π/11), cos(8π/11), ±sin(8π/11)),
  • (cos(2π/11), ±sin(2π/11), cos(10π/11), ±sin(10π/11)),
  • (cos(4π/11), ±sin(4π/11), 1, 0),
  • (cos(4π/11), ±sin(4π/11), cos(2π/11), ±sin(2π/11)),
  • (cos(4π/11), ±sin(4π/11), cos(4π/11), ±sin(4π/11)),
  • (cos(4π/11), ±sin(4π/11), cos(6π/11), ±sin(6π/11)),
  • (cos(4π/11), ±sin(4π/11), cos(8π/11), ±sin(8π/11)),
  • (cos(4π/11), ±sin(4π/11), cos(10π/11), ±sin(10π/11)),
  • (cos(6π/11), ±sin(6π/11), 1, 0),
  • (cos(6π/11), ±sin(6π/11), cos(2π/11), ±sin(2π/11)),
  • (cos(6π/11), ±sin(6π/11), cos(4π/11), ±sin(4π/11)),
  • (cos(6π/11), ±sin(6π/11), cos(6π/11), ±sin(6π/11)),
  • (cos(6π/11), ±sin(6π/11), cos(8π/11), ±sin(8π/11)),
  • (cos(6π/11), ±sin(6π/11), cos(10π/11), ±sin(10π/11)),
  • (cos(8π/11), ±sin(8π/11), 1, 0),
  • (cos(8π/11), ±sin(8π/11), cos(2π/11), ±sin(2π/11)),
  • (cos(8π/11), ±sin(8π/11), cos(4π/11), ±sin(4π/11)),
  • (cos(8π/11), ±sin(8π/11), cos(6π/11), ±sin(6π/11)),
  • (cos(8π/11), ±sin(8π/11), cos(8π/11), ±sin(8π/11)),
  • (cos(8π/11), ±sin(8π/11), cos(10π/11), ±sin(10π/11)),
  • (cos(10π/11), ±sin(10π/11), 1, 0),
  • (cos(10π/11), ±sin(10π/11), cos(2π/11), ±sin(2π/11)),
  • (cos(10π/11), ±sin(10π/11), cos(4π/11), ±sin(4π/11)),
  • (cos(10π/11), ±sin(10π/11), cos(6π/11), ±sin(6π/11)),
  • (cos(10π/11), ±sin(10π/11), cos(8π/11), ±sin(8π/11)),
  • (cos(10π/11), ±sin(10π/11), cos(10π/11), ±sin(10π/11)).

External links[edit | edit source]