# Small hendecagrammic prism

Small hendecagrammic prism
Rank3
TypeUniform
Notation
Bowers style acronymSishenp
Coxeter diagramx x11/2o ()
Elements
Faces11 squares, 2 small hendecagrams
Edges11+22
Vertices22
Vertex figureIsosceles triangle, edge lengths 2, 2, 2cos(2π/11)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {1+{\frac {1}{\sin ^{2}{\frac {2\pi }{11}}}}}}{2}}\approx 1.05134}$
Volume${\displaystyle {\frac {11}{4\tan {\frac {2\pi }{11}}}}\approx 4.27908}$
Dihedral angles4–4: ${\displaystyle {\frac {7\pi }{11}}\approx 114.54545^{\circ }}$
4–11/2: 90°
Height1
Central density2
Number of external pieces24
Level of complexity6
Related polytopes
ArmySemi-uniform Henp, edge lengths ${\displaystyle {\frac {1}{2\cos {\frac {\pi }{11}}}}}$ (base), 1 (sides)
RegimentSishenp
DualSmall hendecagrammic tegum
ConjugatesHendecagonal prism, Hendecagrammic prism, Great hendecagrammic prism, Grand hendecagrammic prism
Convex coreHendecagonal prism
Abstract & topological properties
Flag count132
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryI2(11)×A1, order 44
ConvexNo
NatureTame

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

## Vertex coordinates

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

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