Hendecagonal-dodecagonal duoprism

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Hendecagonal-dodecagonal duoprism
Rank4
TypeUniform
Notation
Bowers style acronymHentwadip
Coxeter diagramx11o x12o ()
Elements
Cells12 hendecagonal prisms, 11 dodecagonal prisms
Faces132 squares, 12 hendecagons, 11 dodecagons
Edges132+132
Vertices132
Vertex figureDigonal disphenoid, edge lengths 2cos(π/11) (base 1), (2+6)/2 (base 2), and 2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angleHenp–11–henp: 150°
Twip–12–twip:
Henp–4–twip: 90°
Central density1
Number of external pieces23
Level of complexity6
Related polytopes
ArmyHentwadip
RegimentHentwadip
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
Abstract & topological properties
Flag count3168
Euler characteristic0
OrientableYes
Properties
SymmetryI2(11)×I2(12), order 528
Flag orbits6
ConvexYes
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:

  • ,
  • ,
  • ,
  • ,
  • ,
  • ,

where j = 2, 4, 6, 8, 10.

Representations[edit | edit source]

A hendecagonal-dodecagonal duoprism has the following Coxeter diagrams:

  • x11o x12o () (full symmetry)
  • x6x x11o () (G2×I2(11) symmetry, dodecagons as dihexagons)

External links[edit | edit source]