# Enneagonal prism

Enneagonal prism
Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymEp
Coxeter diagramx x9o ()
Elements
Faces9 squares, 2 enneagons
Edges9+18
Vertices18
Vertex figureIsosceles triangle, edge lengths 2, 2, 2cos(π/9)
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt{1+\frac{1}{\sin^2\frac\pi9}}}{2} ≈ 1.54504}$
Volume${\displaystyle \frac{9}{4\tan\frac\pi9} ≈ 6.18182}$
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
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryI2(9)×A1, order 36
ConvexYes
NatureTame

The enneagonal 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:

• ${\displaystyle \left(1,\,0,\,±\sin\frac\pi9\right),}$
• ${\displaystyle \left(\cos\left(\frac{2\pi}{9}\right),\,±\sin\left(\frac{2\pi}{9}\right),\,±\sin\frac\pi9\right),}$
• ${\displaystyle \left(\cos\left(\frac{4\pi}{9}\right),\,±\sin\left(\frac{4\pi}{9}\right),\,±\sin\frac\pi9\right),}$
• ${\displaystyle \left(-\frac12,\,±\frac{\sqrt3}{2},\,±\sin\frac\pi9\right),}$
• ${\displaystyle \left(\cos\left(\frac{8\pi}{9}\right),\,±\sin\left(\frac{8\pi}{9}\right),\,±\sin\frac\pi9\right).}$