Hendecagonal-dodecagonal duoprism

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Hendecagonal-dodecagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymHentwadip
Info
Coxeter diagramx11o x12o
SymmetryI2(11)×I2(12), order 528
ArmyHentwadip
RegimentHentwadip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(π/11) (base 1), (2+6)/2 (base 2), and 2 (sides)
Cells12 hendecagonal prisms, 11 dodecagonal prisms
Faces132 squares, 12 hendecagons, 11 dodecagons
Edges132+132
Vertices132
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesHenp–11–henp: 150°
 Twip–12–twip:
 Henp–4–twip: 90°
Central density1
Euler characteristic0
Number of pieces23
Level of complexity6
Related polytopes
DualHendecagonal-dodecagonal duotegum
ConjugatesHendecagonal-dodecagrammic duoprism, Small hendecagrammic-dodecagonal duoprism, Small hendecagrammic-dodecagrammic duoprism, Hendecagrammic-dodecagonal duoprism, Hendecagrammic-dodecagrammic duoprism, Great hendecagrammic-dodecagonal duoprism, Great hendecagrammic-dodecagrammic duoprism, Grand hendecagrammic-dodecagonal duoprism, Grand hendecagrammic-dodecagrammic duoprism
Properties
ConvexYes
OrientableYes
NatureTame

The hendecagonal-dodecagonal duoprism or hentwadip, also known as the 11-12 duoprism, is a uniform duoprism that consists of 11 dodecagonal prisms and 12 hendecagonal prisms, with two of each joining at each vertex.

Vertex coordinates[edit | edit source]

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

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

Representations[edit | edit source]

A hendecagonal-dodecagonal duoprism has the following Coxeter diagrams:

  • x11o x12o (full symmetry)
  • x6x x11o (dodecagons as dihexagons)

External links[edit | edit source]