Square-hendecagrammic duoprism

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Square-hendecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx4o x11/3o
SymmetryBC2×I2(11), order 176
ArmySemi-uniform shendip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(3π/11) (base 1) and 2 (base 2 and sides)
Cells11 cubes, 4 hendecagrammic prisms
Faces11+44 squares, 4 hendecagrams
Edges44+44
Vertices44
Measures (edge length 1)
Circumradius2+csc2(3π/11)/2 ≈ 0.96835
Hypervolume11/[4tan(3π/11)] ≈ 2.38289
Dichoral anglesCube–4–cube: 5π/11 ≈ 81.81818°
 11/3p–11/3–11/3p: 90°
 Cube–4–11/3p: 90°
Central density3
Related polytopes
DualSquare-hendecagrammic duotegum
ConjugatesSquare-hendecagonal duoprism, Square-small hendecagrammic duoprism, Square-great hendecagrammic duoprism, Square-grand hendecagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame


The square-hendecagrammic duoprism, also known as the 4-11/3 duoprism, is a uniform duoprism that consists of 11 cubes and 4 hendecagrammic prisms, with 2 of each meeting at each vertex.

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

Vertex coordinates[edit | edit source]

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

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

External links[edit | edit source]