# Enneagrammic prism

Enneagrammic prism Rank3
TypeUniform
SpaceSpherical
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$\frac{\sqrt{1+\frac{1}{\sin^2\frac{2\pi}{9}}}}{2} ≈ 0.92470$ Volume$\frac{9}{4\tan\frac{2\pi}{9}} ≈ 2.68145$ Dihedral angles4–4: 100°
4–9/2: 90°
Height1
Central density2
Number of external pieces20
Level of complexity6
Related polytopes
ArmySemi-uniform Ep
RegimentStep
DualEnneagrammic tegum
ConjugatesEnneagonal prism, Great enneagrammic prism
Convex coreEnneagonal prism
Abstract & topological properties
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

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)).