Hexagonal-hendecagonal duoprism

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Hexagonal-hendecagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymHahendip
Info
Coxeter diagramx6o x11o
SymmetryG2×I2(11), order 264
ArmyHahendip
RegimentHahendip
Elements
Vertex figureDigonal disphenoid, edge lengths 3 (base 1), 2cos(π/11) (base 2), and 2 (sides)
Cells11 hexagonal prisms, 6 hendecagonal prisms
Faces66 squares, 11 hexagons, 6 hendecagons
Edges66+66
Vertices66
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesHip–6–hip:
 Henp–11–Henp: 120°
 Hip–4–henp: 90°
Central density1
Euler characteristic0
Number of pieces17
Level of complexity6
Related polytopes
DualHexagonal-hendecagonal duotegum
ConjugatesHexagonal-small hendecagrammic duoprism, Hexagonal-hendecagrammic duoprism, Hexagonal-great hendecagrammic duoprism, Hexagonal-grand hendecagrammic duoprism
Properties
ConvexYes
OrientableYes
NatureTame


The hexagonal-hendecagonal duoprism or hahendip, also known as the 6-11 duoprism, is a uniform duoprism that consists of 6 hendecagonal prisms and 11 hexagonal prisms, with two of each joining at each vertex.

Vertex coordinates[edit | edit source]

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

  • (±2sin(π/11), 0, 1, 0),
  • (±2sin(π/11), 0, cos(2π/11), ±sin(2π/11)),
  • (±2sin(π/11), 0, cos(4π/11), ±sin(4π/11)),
  • (±2sin(π/11), 0, cos(6π/11), ±sin(6π/11)),
  • (±2sin(π/11), 0, cos(8π/11), ±sin(8π/11)),
  • (±2sin(π/11), 0, cos(10π/11), ±sin(10π/11)),
  • (±sin(π/11), ±sin(π/11)3, 1, 0),
  • (±sin(π/11), ±sin(π/11)3, cos(2π/11), ±sin(2π/11)),
  • (±sin(π/11), ±sin(π/11)3, cos(4π/11), ±sin(4π/11)),
  • (±sin(π/11), ±sin(π/11)3, cos(6π/11), ±sin(6π/11)),
  • (±sin(π/11), ±sin(π/11)3, cos(8π/11), ±sin(8π/11)),
  • (±sin(π/11), ±sin(π/11)3, cos(10π/11), ±sin(10π/11)).

Representations[edit | edit source]

A hexagonal-hendecagonal duoprism has the following Coxeter diagrams:

  • x6o x11o (full symmetry)
  • x3x x11o (hexagons as ditrigons)

External links[edit | edit source]