Enneagonal prism

Enneagonal prism
(3D model) (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Ep
Coxeter diagram	x x9o ()
Elements
Faces	9 squares, 2 enneagons
Edges	9+18
Vertices	18
Vertex figure	Isosceles triangle, edge lengths √2, √2, 2cos(π/9)
Measures (edge length 1)
Circumradius	$\frac{\sqrt{1+\frac{1}{\sin^2\frac\pi9}}}{2} ≈ 1.54504$
Volume	$\frac{9}{4\tan\frac\pi9} ≈ 6.18182$
Dihedral angles	4–4: 140°
	4–9: 90°
Height	1
Central density	1
Number of external pieces	11
Level of complexity	3
Related polytopes
Army	Ep
Regiment	Ep
Dual	Enneagonal tegum
Conjugates	Enneagrammic prism, Great enneagrammic prism
Abstract & topological properties
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	I2(9)×A1, order 36
Convex	Yes
Nature	Tame

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:

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

External links

• Wikipedia Contributors. "Enneagonal prism".