Hendecagrammic prism

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Hendecagrammic prism
Prism 11-3.png
Rank3
TypeUniform
SpaceSpherical
Info
Coxeter diagramx x11/3o
SymmetryI2(11)×A1, order 44
ArmySemi-uniform hendecagonal prism
RegimentHendecagrammic prism
Elements
Vertex figureIsosceles triangle, edge lengths 2, 2, 2cos(3π/11)
Faces11 squares, 2 hendecagrams
Edges11+22
Vertices22
Measures (edge length 1)
Circumradius1+1/sin2(3π/11)/2 ≈ 0.82928
Volume11/(4tan(3π/11)) ≈ 2.38289
Dihedral angles4–11/3: 90°
 4–4: 5π/11 ≈ 81.81818°
Height1
Central density3
Euler characteristic2
Related polytopes
DualHendecagrammic bipyramid
ConjugatesHendecagonal prism, Small hendecagrammic prism, Great hendecagrammic prism, Grand hendecagrammic prism
Properties
ConvexNo
OrientableYes
NatureTame

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

Vertex coordinates[edit | edit source]

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

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