# Small hendecagrammic-grand hendecagrammic duoprism

Small hendecagrammic-grand hendecagrammic duoprism
Rank4
TypeUniform
Notation
Coxeter diagramx11/2o x11/5o ()
Elements
Cells11 small hendecagrammic prisms, 11 grand hendecagrammic prisms
Faces121 squares, 11 small hendecagrams, 11 grand hendecagrams
Edges121+121
Vertices121
Vertex figureDigonal disphenoid, edge lengths 2cos(2π/11) (base 1), 2cos(5π/11) (base 2), 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {{\frac {1}{4\sin ^{2}{\frac {2\pi }{11}}}}+{\frac {1}{4\sin ^{2}{\frac {5\pi }{11}}}}}}\approx 1.05379}$
Hypervolume${\displaystyle {\frac {121}{16\tan {\frac {2\pi }{11}}\tan {\frac {5\pi }{11}}}}\approx 1.69191}$
Dichoral anglesGashenp–11/5–gashenp: ${\displaystyle {\frac {7\pi }{11}}\approx 114.54545^{\circ }}$
Sishenp–4–gashenp: 90°
Sishenp–11/2–sishenp: ${\displaystyle {\frac {\pi }{11}}\approx 16.36364^{\circ }}$
Central density10
Number of external pieces44
Level of complexity24
Related polytopes
ArmySemi-uniform handip
DualSmall hendecagrammic-grand hendecagrammic duotegum
ConjugatesHendecagonal-small hendecagrammic duoprism, Hendecagonal-hendecagrammic duoprism, Hendecagonal-great hendecagrammic duoprism, Hendecagonal-grand hendecagrammic duoprism, Small hendecagrammic-hendecagrammic duoprism, Small hendecagrammic-great hendecagrammic duoprism, Hendecagrammic-great hendecagrammic duoprism, Hendecagrammic-grand hendecagrammic duoprism, Great hendecagrammic-grand hendecagrammic duoprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(11)×I2(11), order 484
ConvexNo
NatureTame

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

## Coordinates

The vertex coordinates of a small hendecagrammic-grand hendecagrammic duoprism, centered at the origin and with edge length 4sin(2π/11)sin(5π/11), are given by:

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

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