Hendecagonal prism

Hendecagonal prism
(3D model) (OFF file)
Rank	3
Type	Uniform
Notation
Bowers style acronym	Henp
Coxeter diagram	x2x11o ()
Conway notation	P11
Elements
Faces	11 squares, 2 hendecagons
Edges	11+22
Vertices	22
Vertex figure	Isosceles triangle, edge lengths √2, √2, 2cos(π/11)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {1+{\frac {1}{\sin ^{2}{\frac {\pi }{11}}}}}}{2}}\approx 1.84382$
Volume	${\frac {11}{4\tan {\frac {\pi }{11}}}}\approx 9.36564$
Dihedral angles	4–4: ${\frac {9\pi }{11}}\approx 147.27273^{\circ }$
	4–11: 90°
Height	1
Central density	1
Number of external pieces	13
Level of complexity	3
Related polytopes
Army	Henp
Regiment	Henp
Dual	Hendecagonal tegum
Conjugates	Small hendecagrammic prism, Hendecagrammic prism, Great hendecagrammic prism, Grand hendecagrammic prism
Abstract & topological properties
Flag count	132
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Skeleton	GP(11,1)
Properties
Symmetry	I2(11)×A1, order 44
Convex	Yes
Nature	Tame

The hendecagonal prism or henp is a prismatic uniform polyhedron. It consists of 2 hendecagons and 11 squares. Each vertex joins one hendecagon and two squares. As the name suggests, it is a prism based on a hendecagon.

Vertex coordinates

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

• $\left(1,\,0,\,\pm \sin {\frac {\pi }{11}}\right)$,
• $\left(\cos \left({\frac {2\pi }{11}}\right),\,\pm \sin \left({\frac {2\pi }{11}}\right),\,\pm \sin {\frac {\pi }{11}}\right)$,
• $\left(\cos \left({\frac {4\pi }{11}}\right),\,\pm \sin \left({\frac {4\pi }{11}}\right),\,\pm \sin {\frac {\pi }{11}}\right)$,
• $\left(\cos \left({\frac {6\pi }{11}}\right),\,\pm \sin \left({\frac {6\pi }{11}}\right),\,\pm \sin {\frac {\pi }{11}}\right)$,
• $\left(\cos \left({\frac {8\pi }{11}}\right),\,\pm \sin \left({\frac {8\pi }{11}}\right),\,\pm \sin {\frac {\pi }{11}}\right)$,
• $\left(\cos \left({\frac {10\pi }{11}}\right),\,\pm \sin \left({\frac {10\pi }{11}}\right),\,\pm \sin {\frac {\pi }{11}}\right)$.

External links

• Wikipedia contributors. "Hendecagonal prism".