# Hendecagonal-small hendecagrammic duoprism

Hendecagonal-small hendecagrammic duoprism
Rank4
TypeUniform
Notation
Coxeter diagramx11o x11/2o (          )
Elements
Cells11 hendecagonal prisms, 11 small hendecagrammic prisms
Faces121 squares, 11 hendecagons, 11 small hendecagrams
Edges121+121
Vertices121
Vertex figureDigonal disphenoid, edge lengths 2cos(π/11) (base 1), 2cos(2π/11) (base 2), 2 (sides)
Measures (edge length 1)
Circumradius${\sqrt {\frac {4\cos ^{2}{\frac {\pi }{11}}+1}{4\sin ^{2}{\frac {2\pi }{11}}}}}\approx 2.00125$ Hypervolume$121{\frac {1-\tan ^{2}{\frac {\pi }{11}}}{32\tan ^{2}{\frac {\pi }{11}}}}\approx 40.07636$ Dichoral anglesSishenp–11/2–sishenp: ${\frac {9\pi }{11}}\approx 147.27273^{\circ }$ Henp–11–henp: ${\frac {7\pi }{11}}\approx 114.54545^{\circ }$ Henp–4–sishenp: 90°
Central density2
Number of external pieces33
Level of complexity12
Related polytopes
ArmySemi-uniform handip
DualHendecagonal-small hendecagrammic duotegum
ConjugatesHendecagonal-hendecagrammic duoprism, Hendecagonal-great hendecagrammic duoprism, Hendecagonal-grand hendecagrammic duoprism, Small hendecagrammic-hendecagrammic duoprism, Small hendecagrammic-great hendecagrammic duoprism, Small hendecagrammic-grand hendecagrammic duoprism, Hendecagrammic-great hendecagrammic duoprism, Hendecagrammic-grand hendecagrammic duoprism, Great hendecagrammic-grand hendecagrammic duoprism
Abstract & topological properties
Flag count2904
Euler characteristic0
OrientableYes
Properties
SymmetryI2(11)×I2(11), order 484
ConvexNo
NatureTame

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

## Vertex coordinates

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

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

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