Enneagrammic prism

Enneagrammic prism
(3D model) (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Step
Coxeter diagram	x x9/2o ()
Elements
Faces	9 squares, 2 enneagrams
Edges	9+18
Vertices	18
Vertex figure	Isosceles 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 angles	4–4: 100°
	4–9/2: 90°
Height	1
Central density	2
Number of external pieces	20
Level of complexity	6
Related polytopes
Army	Semi-uniform Ep
Regiment	Step
Dual	Enneagrammic tegum
Conjugates	Enneagonal prism, Great enneagrammic prism
Convex core	Enneagonal prism
Abstract & topological properties
Euler characteristic	2
Orientable	Yes
Genus	0
Properties
Symmetry	I2(9)×A1, order 36
Convex	No
Nature	Tame

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)).

External links

• Wikipedia Contributors. "Enneagrammic prism".