# Hexagonal-small hendecagrammic duoprism

Hexagonal-small hendecagrammic duoprism
Rank4
TypeUniform
Notation
Coxeter diagramx6o x11/2o ()
Elements
Cells11 hexagonal prisms, 6 small hendecagrammic prisms
Faces66 squares, 11 hexagons, 6 small hendecagrams
Edges66+66
Vertices66
Vertex figureDigonal disphenoid, edge lengths 3 (base 1), 2cos(2π/11) (base 2), 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {4+{\frac {1}{4\sin ^{2}{\frac {2\pi }{11}}}}}}{2}}\approx 1.36210}$
Hypervolume${\displaystyle {\frac {33{\sqrt {3}}}{8\tan {\frac {2\pi }{11}}}}\approx 11.11739}$
Dichoral anglesSishenp–11/2–sishenp: 120°
Hip–6–hip: ${\displaystyle {\frac {7\pi }{11}}\approx 114.54545^{\circ }}$
Hip–4–sishenp: 90°
Central density2
Number of external pieces28
Level of complexity12
Related polytopes
ArmySemi-uniform hahendip
DualHexagonal-small hendecagrammic duotegum
ConjugatesHexagonal-hendecagonal duoprism, Hexagonal-hendecagrammic duoprism, Hexagonal-great hendecagrammic duoprism, Hexagonal-grand hendecagrammic duoprism
Abstract & topological properties
Flag count1584
Euler characteristic0
OrientableYes
Properties
SymmetryG2×I2(11), order 264
ConvexNo
NatureTame

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

## Vertex coordinates

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

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

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

## Representations

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