# Grand hendecagrammic prism

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.

Grand hendecagrammic prism
Rank3
TypeUniform
Notation
Bowers style acronymGashenp
Coxeter diagramx x11/5o ()
Elements
Faces11 squares, 2 grand hendecagrams
Edges11+22
Vertices22
Vertex figureIsosceles triangle, edge lengths 2, 2, 2cos(5π/11)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {1+{\frac {1}{\sin ^{2}{\frac {5\pi }{11}}}}}}{2}}\approx 0.71075}$
Volume${\displaystyle {\frac {11}{4\tan {\frac {5\pi }{11}}}}\approx 0.39539}$
Dihedral angles4–11/5: 90°
4–4: ${\displaystyle {\frac {\pi }{11}}\approx 16.36364^{\circ }}$
Height1
Central density5
Number of external pieces24
Level of complexity6
Related polytopes
ArmySemi-uniform Henp, edge lengths ${\displaystyle 2\cos {\frac {5\pi }{11}}}$ (base), 1 (sides)
RegimentGashenp
DualGrand hendecagrammic tegum
ConjugatesHendecagonal prism, Small hendecagrammic prism, Hendecagrammic prism, Great hendecagrammic prism
Convex coreHendecagonal prism
Abstract & topological properties
Flag count132
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryI2(11)×A1, order 44
ConvexNo
NatureTame

## 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)).