# Hendecagonal prism

Hendecagonal prism
Rank3
TypeUniform
Notation
Bowers style acronymHenp
Coxeter diagramx2x11o ()
Conway notationP11
Elements
Faces11 squares, 2 hendecagons
Edges11+22
Vertices22
Vertex figureIsosceles triangle, edge lengths 2, 2, 2cos(π/11)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {1+{\frac {1}{\sin ^{2}{\frac {\pi }{11}}}}}}{2}}\approx 1.84382}$
Volume${\displaystyle {\frac {11}{4\tan {\frac {\pi }{11}}}}\approx 9.36564}$
Dihedral angles4–4: ${\displaystyle {\frac {9\pi }{11}}\approx 147.27273^{\circ }}$
4–11: 90°
Height1
Central density1
Number of external pieces13
Level of complexity3
Related polytopes
ArmyHenp
RegimentHenp
DualHendecagonal tegum
ConjugatesSmall hendecagrammic prism, Hendecagrammic prism, Great hendecagrammic prism, Grand hendecagrammic prism
Abstract & topological properties
Flag count132
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
SkeletonGP(11,1)
Properties
SymmetryI2(11)×A1, order 44
ConvexYes
NatureTame

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:

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