Great heptagrammic-hendecagonal duoprism

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Great heptagrammic-hendecagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx7/3o x11o
SymmetryI2(7)×I2(11), order 308
ArmySemi-uniform hehendip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(3π/7) (base 1), 2cos(π/11) (base 2), 2 (sides)
Cells11 great heptagrammic prisms, 7 hendecagonal prisms
Faces77 squares, 11 great heptagrams, 7 hendecagons
Edges77+77
Vertices77
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesGiship–7/3–giship: 9π/11 ≈ 147.27273°
 11p–11–11p: π/7 ≈ 25.71429°
 Giship–4–11p: 90°
Central density3
Related polytopes
DualGreat heptagrammic-hendecagonal 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-small hendecagrammic duoprism, Great heptagrammic-hendecagrammic duoprism, Great heptagrammic-great hendecagrammic duoprism, Great heptagrammic-grand hendecagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame


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

Vertex coordinates[edit | edit source]

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

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

External links[edit | edit source]