# Hendecagonal prism

Hendecagonal prism Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymHenp
Coxeter diagramx x11o (     )
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$\frac{\sqrt{1+\frac{1}{\sin^2\frac{\pi}{11}}}}{2} ≈ 1.84382$ Volume$\frac{11}{4\tan\frac{\pi}{11}} ≈ 9.36564$ Dihedral angles4–4: $\frac{9\pi}{11} ≈ 147.27273^\circ$ 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
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:

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