Small hendecagrammic prism

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Small hendecagrammic prism
Prism 11-2.png
Rank3
TypeUniform
SpaceSpherical
Info
Coxeter diagramx x11/2o
SymmetryI2(11)×A1, order 44
ArmySemi-uniform hendecagonal prism
RegimentSmall hendecagrammic prism
Elements
Vertex figureIsosceles triangle, edge lengths 2, 2, 2cos(2π/11)
Faces11 squares, 2 small hendecagrams
Edges11+22
Vertices22
Measures (edge length 1)
Circumradius1+1/sin2(2π/11)/2 ≈ 1.05134
Volume11/(4tan(2π/11)) ≈ 4.27908
Dihedral angles4–11/2: 90°
 4–4: 7π/11 ≈ 114.54545°
Height1
Central density2
Euler characteristic2
Related polytopes
DualSmall hendecagrammic bipyramid
ConjugatesHendecagonal prism, Hendecagrammic prism, Great hendecagrammic prism, Grand hendecagrammic prism
Properties
ConvexNo
OrientableYes
NatureTame

The small hendecagrammic prism is a prismatic uniform polyhedron. It consists of 2 small hendecagrams and 11 squares. Each vertex joins one small hendecagram and two squares. As the name suggests, it is a prism based on a small hendecagram.

Vertex coordinates[edit | edit source]

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

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