# Great enneagrammic prism

Great enneagrammic prism
Rank3
TypeUniform
Notation
Bowers style acronymGistep
Coxeter diagramx x9/4o ()
Elements
Faces9 squares, 2 great enneagrams
Edges9+18
Vertices18
Vertex figureIsosceles triangle, edge lengths 2, 2, 2cos(4π/9)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {1+{\frac {1}{\sin ^{2}{\frac {4\pi }{9}}}}}}{2}}\approx 0.71258}$
Volume${\displaystyle {\frac {9}{4\tan {\frac {4\pi }{9}}}}\approx 0.39674}$
Dihedral angles4–9/4: 90°
4–4: 20°
Height1
Central density4
Number of external pieces20
Level of complexity6
Related polytopes
ArmySemi-uniform Ep, edge lengths ${\displaystyle 2\cos {\frac {4\pi }{9}}}$ (base), 1 (sides)
RegimentGistep
DualGreat enneagrammic tegum
ConjugatesEnneagonal prism, Enneagrammic prism
Convex coreenneagonal prism
Abstract & topological properties
Flag count108
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryI2(9)×A1, order 36
ConvexNo
NatureTame

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

## Vertex coordinates

The coordinates of a great enneagrammic prism, centered at the origin and with edge length 2sin(4π/9), are given by:

• (1, 0, \pmsin(4π/9)),
• (cos(2π/9), \pmsin(2π/9), \pmsin(4π/9)),
• (cos(4π/9), \pmsin(4π/9), \pmsin(4π/9)),
• (–1/2, \pm3/2), \pmsin(4π/9)),
• (cos(8π/9), \pmsin(8π/9), \pmsin(4π/9)).