Great heptagrammic-hendecagrammic duoprism

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Great heptagrammic-hendecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx7/3o x11/3o
SymmetryI2(7)×I2(11), order 308
ArmySemi-uniform hehendip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(3π/7) (base 1), 2cos(3π/11) (base 2), 2 (sides)
Cells11 great heptagrammic prisms, 7 hendecagrammic prisms
Faces77 squares, 11 great heptagrams, 7 hendecagrams
Edges77+77
Vertices77
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesGiship–7/3–giship: 5π/11 ≈ 81.81818°
 11/3p–11/3–11/3p: π/7 ≈ 25.71429°
 Giship–4–11/3p: 90°
Central density9
Related polytopes
DualGreat heptagrammic-hendecagrammic duotegum
ConjugatesHeptagonal-hendecagonal duoprism, Heptagonal-small hendecagrammic duoprism, Heptagonal-hendecagrammic duoprism, Heptagonal-great hendecagrammic duoprism, Heptagonal-grand hendecagrammic duoprism, Heptagrammic-hendecagonal duoprism, Heptagrammic-small hendecagrammic duoprism, Heptagrammic-hendecagrammic duoprism, Heptagrammic-great hendecagrammic duoprism, Heptagrammic-grand hendecagrammic duoprism, Great heptagrammic-hendecagonal duoprism, Great heptagrammic-small hendecagrammic duoprism, Great heptagrammic-great hendecagrammic duoprism, Great heptagrammic-grand hendecagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame


The great heptagrammic-hendecagrammic duoprism, also known as the 7/3-11/3 duoprism, is a uniform duoprism that consists of 11 great heptagrammic prisms and 7 hendecagrammic prisms, with 2 of each meeting at each vertex.

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

Vertex coordinates[edit | edit source]

The coordinates of a great heptagrammic-hendecagrammic duoprism, centered at the origin and with edge length 4sin(3π/7)sin(3π/11), are given by:

  • (2sin(3π/11), 0, 2sin(3π/7), 0),
  • (2sin(3π/11), 0, 2sin(3π/7)cos(2π/11), ±2sin(3π/7)sin(2π/11)),
  • (2sin(3π/11), 0, 2sin(3π/7)cos(4π/11), ±2sin(3π/7)sin(4π/11)),
  • (2sin(3π/11), 0, 2sin(3π/7)cos(6π/11), ±2sin(3π/7)sin(6π/11)),
  • (2sin(3π/11), 0, 2sin(3π/7)cos(8π/11), ±2sin(3π/7)sin(8π/11)),
  • (2sin(3π/11), 0, 2sin(3π/7)cos(10π/11), ±2sin(3π/7)sin(10π/11)),
  • (2sin(3π/11)cos(2π/7), ±2sin(3π/11)sin(2π/7), 2sin(3π/7), 0),
  • (2sin(3π/11)cos(2π/7), ±2sin(3π/11)sin(2π/7), 2sin(3π/7)cos(2π/11), ±2sin(3π/7)sin(2π/11)),
  • (2sin(3π/11)cos(2π/7), ±2sin(3π/11)sin(2π/7), 2sin(3π/7)cos(4π/11), ±2sin(3π/7)sin(4π/11)),
  • (2sin(3π/11)cos(2π/7), ±2sin(3π/11)sin(2π/7), 2sin(3π/7)cos(6π/11), ±2sin(3π/7)sin(6π/11)),
  • (2sin(3π/11)cos(2π/7), ±2sin(3π/11)sin(2π/7), 2sin(3π/7)cos(8π/11), ±2sin(3π/7)sin(8π/11)),
  • (2sin(3π/11)cos(2π/7), ±2sin(3π/11)sin(2π/7), 2sin(3π/7)cos(10π/11), ±2sin(3π/7)sin(10π/11)),
  • (2sin(3π/11)cos(4π/7), ±2sin(3π/11)sin(4π/7), 2sin(3π/7), 0),
  • (2sin(3π/11)cos(4π/7), ±2sin(3π/11)sin(4π/7), 2sin(3π/7)cos(2π/11), ±2sin(3π/7)sin(2π/11)),
  • (2sin(3π/11)cos(4π/7), ±2sin(3π/11)sin(4π/7), 2sin(3π/7)cos(4π/11), ±2sin(3π/7)sin(4π/11)),
  • (2sin(3π/11)cos(4π/7), ±2sin(3π/11)sin(4π/7), 2sin(3π/7)cos(6π/11), ±2sin(3π/7)sin(6π/11)),
  • (2sin(3π/11)cos(4π/7), ±2sin(3π/11)sin(4π/7), 2sin(3π/7)cos(8π/11), ±2sin(3π/7)sin(8π/11)),
  • (2sin(3π/11)cos(4π/7), ±2sin(3π/11)sin(4π/7), 2sin(3π/7)cos(10π/11), ±2sin(3π/7)sin(10π/11)),
  • (2sin(3π/11)cos(6π/7), ±2sin(3π/11)sin(6π/7), 2sin(3π/7), 0),
  • (2sin(3π/11)cos(6π/7), ±2sin(3π/11)sin(6π/7), 2sin(3π/7)cos(2π/11), ±2sin(3π/7)sin(2π/11)),
  • (2sin(3π/11)cos(6π/7), ±2sin(3π/11)sin(6π/7), 2sin(3π/7)cos(4π/11), ±2sin(3π/7)sin(4π/11)),
  • (2sin(3π/11)cos(6π/7), ±2sin(3π/11)sin(6π/7), 2sin(3π/7)cos(6π/11), ±2sin(3π/7)sin(6π/11)),
  • (2sin(3π/11)cos(6π/7), ±2sin(3π/11)sin(6π/7), 2sin(3π/7)cos(8π/11), ±2sin(3π/7)sin(8π/11)),
  • (2sin(3π/11)cos(6π/7), ±2sin(3π/11)sin(6π/7), 2sin(3π/7)cos(10π/11), ±2sin(3π/7)sin(10π/11)).

External links[edit | edit source]