Enneagrammic prism

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Enneagrammic prism
Prism 9-2.png
Rank3
TypeUniform
SpaceSpherical
Bowers style acronymStep
Info
Coxeter diagramx x9/2o
SymmetryI2(9)×A1, order 36
ArmySemi-uniform Ep
RegimentStep
Elements
Vertex figureIsosceles triangle, edge lengths 2, 2, 2cos(2π/9)
Faces9 squares, 2 enneagrams
Edges9+18
Vertices18
Measures (edge length 1)
Circumradius1+1/sin2(2π/9)/2 ≈ 0.92470
Volume9/(4tan(2π/9)) ≈ 2.68145
Dihedral angles4–9/2: 90°
 4–4: 100°
Height1
Central density2
Euler characteristic2
Related polytopes
DualEnneagrammic bipyramid
ConjugatesEnneagonal prism, Great enneagrammic prism
Properties
ConvexNo
OrientableYes
NatureTame

The enneagrammic prism, or step, is a prismatic uniform polyhedron. It consists of 2 enneagrams and 9 squares. Each vertex joins one enneagram and two squares. As the name suggests, it is a prism based on an ennearam.

Vertex coordinates[edit | edit source]

The coordinates of an enneagrammic prism, centered at the origin and with edge length 2sin(2π/9), are given by:

  • (1, 0, ±sin(2π/9)),
  • (cos(2π/9), ±sin(2π/9), ±sin(2π/9)),
  • (cos(4π/9), ±sin(4π/9), ±sin(2π/9)),
  • (–1/2, ±3/2, ±sin(2π/9)),
  • (cos(8π/9), ±sin(8π/9), ±sin(2π/9)).

External links[edit | edit source]