# Hexagonal-grand hendecagrammic duoprism

Hexagonal-grand hendecagrammic duoprism
Rank4
TypeUniform
Notation
Coxeter diagramx6o x11/5o ()
Elements
Cells11 hexagonal prisms, 6 grand hendecagrammic prisms
Faces66 squares, 11 hexagons, 6 grand hendecagrams
Edges66+66
Vertices66
Vertex figureDigonal disphenoid, edge lengths 3 (base 1), 2cos(5π/11) (base 2), 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {1+{\frac {1}{4\sin ^{2}{\frac {5\pi }{11}}}}}}\approx 1.12034}$
Hypervolume${\displaystyle {\frac {33{\sqrt {3}}}{8\tan {\frac {5\pi }{11}}}}\approx 1.02725}$
Dichoral anglesGashenp–11/5–gashenp: 120°
Hip–4–gashenp: 90°
Hip–6–hip: ${\displaystyle {\frac {\pi }{11}}\approx 16.36364^{\circ }}$
Central density5
Number of external pieces28
Level of complexity12
Related polytopes
ArmySemi-uniform hahendip
DualHexagonal-grand hendecagrammic duotegum
ConjugatesHexagonal-hendecagonal duoprism, Hexagonal-small hendecagrammic duoprism, Hexagonal-hendecagrammic duoprism, Hexagonal-great hendecagrammic duoprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryG2×I2(11), order 264
ConvexNo
NatureTame

The hexagonal-grand hendecagrammic duoprism, also known as the 6-11/5 duoprism, is a uniform duoprism that consists of 11 hexagonal prisms and 6 grand hendecagrammic prisms, with 2 of each at each vertex.

## Vertex coordinates

The coordinates of a hexagonal-grand hendecagrammic duoprism, centered at the origin and with edge length 2sin(5π/11), are given by:

• ${\displaystyle \left(\pm 2\sin {\frac {5\pi }{11}},\,0,\,1,\,0\right),}$
• ${\displaystyle \left(\pm 2\sin {\frac {5\pi }{11}},\,0,\,\cos \left({\frac {j\pi }{11}}\right),\,\pm \sin \left({\frac {j\pi }{11}}\right)\right),}$
• ${\displaystyle \left(\pm \sin {\frac {5\pi }{11}},\,\pm {\sqrt {3}}\sin {\frac {5\pi }{11}},\,1,\,0\right),}$
• ${\displaystyle \left(\pm \sin {\frac {5\pi }{11}},\,\pm {\sqrt {3}}\sin {\frac {5\pi }{11}},\,\cos \left({\frac {j\pi }{11}}\right),\,\pm \sin \left({\frac {j\pi }{11}}\right)\right),}$

where j = 2, 4, 6, 8, 10.

## Representations

A hexagonal-grand hendecagrammic duoprism has the following Coxeter diagrams: