Enneagrammic prism

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Enneagrammic prism
Rank3
TypeUniform
Notation
Bowers style acronymStep
Coxeter diagramx x9/2o ()
Elements
Faces9 squares, 2 enneagrams
Edges9+18
Vertices18
Vertex figureIsosceles triangle, edge lengths 2, 2, 2cos(2π/9)
Measures (edge length 1)
Circumradius
Volume
Dihedral angles4–4: 100°
 4–9/2: 90°
Height1
Central density2
Number of external pieces20
Level of complexity6
Related polytopes
ArmySemi-uniform Ep, edge lengths (base), 1 (sides)
RegimentStep
DualEnneagrammic tegum
ConjugatesEnneagonal prism, Great enneagrammic prism
Convex coreEnneagonal prism
Abstract & topological properties
Flag count108
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryI2(9)×A1, order 36
ConvexNo
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, \pmsin(2π/9)),
  • (cos(2π/9), \pmsin(2π/9), \pmsin(2π/9)),
  • (cos(4π/9), \pmsin(4π/9), \pmsin(2π/9)),
  • (–1/2, \pm3/2, \pmsin(2π/9)),
  • (cos(8π/9), \pmsin(8π/9), \pmsin(2π/9)).

External links[edit | edit source]