Square-small hendecagrammic duoprism

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Square-small hendecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx4o x11/2o
SymmetryBC2×I2(11), order 176
ArmySemi-uniform shendip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(2π/11) (base 1) and 2 (base 2 and sides)
Cells11 cubes, 4 small hendecagrammic prisms
Faces11+44 squares, 4 small hendecagrams
Edges44+44
Vertices44
Measures (edge length 1)
Circumradius2+csc2(2π/11)/2 ≈ 1.16418
Hypervolume11/[4tan(2π/11)] ≈ 4.27908
Dichoral anglesCube–4–cube: 7π/11 ≈ 114.54545°
 11/2p–11/2–11/2p: 90°
 Cube–4–11/2p: 90°
Central density2
Related polytopes
DualSquare-small hendecagrammic duotegum
ConjugatesSquare-hendecagonal duoprism, Square-hendecagrammic duoprism, Square-great hendecagrammic duoprism, Square-grand hendecagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame


The square-small hendecagrammic duoprism, also known as the 4-11/2 duoprism, is a uniform duoprism that consists of 11 cubes and 4 small hendecagrammic prisms, with 2 of each meeting at each vertex.

Vertex coordinates[edit | edit source]

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

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

External links[edit | edit source]