# Enneagonal prism

Enneagonal prism
Rank3
TypeUniform
Notation
Bowers style acronymEp
Coxeter diagram
Conway notationP9
Elements
Faces9 squares, 2 enneagons
Edges9+18
Vertices18
Vertex figureIsosceles triangle, edge lengths 2, 2, 2cos(π/9)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {1+{\frac {1}{\sin ^{2}{\frac {\pi }{9}}}}}}{2}}\approx 1.54504}$
Volume${\displaystyle {\frac {9}{4\tan {\frac {\pi }{9}}}}\approx 6.18182}$
Dihedral angles4–4: 140°
4–9: 90°
Height1
Central density1
Number of external pieces11
Level of complexity3
Related polytopes
ArmyEp
RegimentEp
DualEnneagonal tegum
ConjugatesEnneagrammic prism, Great enneagrammic prism
Abstract & topological properties
Flag count108
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
SkeletonGP(9,1)
Properties
SymmetryI2(9)×A1, order 36
ConvexYes
NatureTame

The enneagonal prism, nonagonal prism, or ep, is a prismatic uniform polyhedron. It consists of 2 enneagons and 9 squares. Each vertex joins one enneagon and two squares. As the name suggests, it is a prism based on an enneagon.

## Vertex coordinates

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

• ${\displaystyle \left(1,\,0,\,\pm \sin {\frac {\pi }{9}}\right)}$,
• ${\displaystyle \left(\cos \left({\frac {2\pi }{9}}\right),\,\pm \sin \left({\frac {2\pi }{9}}\right),\,\pm \sin {\frac {\pi }{9}}\right)}$,
• ${\displaystyle \left(\cos \left({\frac {4\pi }{9}}\right),\,\pm \sin \left({\frac {4\pi }{9}}\right),\,\pm \sin {\frac {\pi }{9}}\right)}$,
• ${\displaystyle \left(-{\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,\pm \sin {\frac {\pi }{9}}\right)}$,
• ${\displaystyle \left(\cos \left({\frac {8\pi }{9}}\right),\,\pm \sin \left({\frac {8\pi }{9}}\right),\,\pm \sin {\frac {\pi }{9}}\right)}$.