Hendecagrammic-dodecagonal duoprism

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Hendecagrammic-dodecagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx11/3o x12o
SymmetryI2(11)×I2(12), order 528
ArmySemi-uniform hentwadip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(3π/11) (base 1), (6+2)/2 (base 2), 2 (sides)
Cells12 hendecagrammic prisms, 11 dodecagonal prisms
Faces132 squares, 12 hendecagrams, 11 dodecagons
Edges132+132
Vertices132
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles11/3p–11/3–11/3p: 150°
 Twip–12–twip: 5π/11 ≈ 81.81818°
 11/3p–4–twip: 90°
Central density3
Related polytopes
DualHendecagrammic-dodecagonal duotegum
ConjugatesHendecagonal-dodecagonal duoprism, Hendecagonal-dodecagrammic duoprism, Small hendecagrammic-dodecagonal duoprism, Small hendecagrammic-dodecagrammic duoprism, Hendecagrammic-dodecagrammic duoprism, Great hendecagrammic-dodecagonal duoprism, Great hendecagrammic-dodecagrammic duoprism, Grand hendecagrammic-dodecagonal duoprism, Grand hendecagrammic-dodecagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame


The hendecagrammic-dodecagonal duoprism, also known as the 11/3-12 duoprism, is a uniform duoprism that consists of 12 hendecagrammic prisms and 11 dodecagonal prisms, with 2 of each meeting at each vertex.

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

Vertex coordinates[edit | edit source]

The coordinates of a hendecagrammic-dodecagonal duoprism, centered at the origin and with edge length 2sin(3π/11), are given by:

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

External links[edit | edit source]