Grand hendecagrammic prism

Grand hendecagrammic prism
(3D model) (OFF file)
Rank	3
Type	Uniform
Notation
Bowers style acronym	Gashenp
Coxeter diagram	x x11/5o ()
Elements
Faces	11 squares, 2 grand hendecagrams
Edges	11+22
Vertices	22
Vertex figure	Isosceles triangle, edge lengths √2, √2, 2cos(5π/11)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {1+{\frac {1}{\sin ^{2}{\frac {5\pi }{11}}}}}}{2}}\approx 0.71075$
Volume	${\frac {11}{4\tan {\frac {5\pi }{11}}}}\approx 0.39539$
Dihedral angles	4–11/5: 90°
	4–4: ${\frac {\pi }{11}}\approx 16.36364^{\circ }$
Height	1
Central density	5
Number of external pieces	24
Level of complexity	6
Related polytopes
Army	Semi-uniform Henp, edge lengths $2\cos {\frac {5\pi }{11}}$ (base), 1 (sides)
Regiment	Gashenp
Dual	Grand hendecagrammic tegum
Conjugates	Hendecagonal prism, Small hendecagrammic prism, Hendecagrammic prism, Great hendecagrammic prism
Convex core	Hendecagonal prism
Abstract & topological properties
Flag count	132
Euler characteristic	2
Orientable	Yes
Genus	0
Properties
Symmetry	I2(11)×A1, order 44
Convex	No
Nature	Tame

The grand hendecagrammic prism or gashenp is a prismatic uniform polyhedron. It consists of 2 grand hendecagrams and 11 squares. Each vertex joins one grand hendecagram and two squares. As the name suggests, it is a prism based on a grand hendecagram.

Vertex coordinates

The coordinates of a grand hendecagrammic prism, centered at the origin and with edge length 2sin(5π/11), are given by:

• (1, 0, \pmsin(5π/11)),
• (cos(2π/11), \pmsin(2π/11), \pmsin(5π/11)),
• (cos(4π/11), \pmsin(4π/11), \pmsin(5π/11)),
• (cos(6π/11), \pmsin(6π/11), \pmsin(5π/11)),
• (cos(8π/11), \pmsin(8π/11), \pmsin(5π/11)),
• (cos(10π/11), \pmsin(10π/11), \pmsin(5π/11)).