# Hendecagrammic-grand hendecagrammic duoprism

Hendecagrammic-grand hendecagrammic duoprism
Rank4
TypeUniform
Notation
Coxeter diagramx11/3o x11/5o (             )
Elements
Cells11 hendecagrammic prisms, 11 grand hendecagrammic prisms
Faces121 squares, 11 hendecagrams, 11 grand hendecagrams
Edges121+121
Vertices121
Vertex figureDigonal disphenoid, edge lengths 2cos(3π/11) (base 1), 2cos(5π/11) (base 2), 2 (sides)
Measures (edge length 1)
Circumradius${\sqrt {{\frac {1}{4\sin ^{2}{\frac {3\pi }{11}}}}+{\frac {1}{4\sin ^{2}{\frac {5\pi }{11}}}}}}\approx 0.83239$ Hypervolume${\frac {121}{16\tan {\frac {3\pi }{11}}\tan {\frac {5\pi }{11}}}}\approx 0.94217$ Dichoral anglesShenp–4–gashenp: 90°
Gashenp–11/5–gashenp: ${\frac {5\pi }{11}}\approx 81.81818^{\circ }$ Shenp–11/3–shenp: ${\frac {\pi }{11}}\approx 16.36364^{\circ }$ Central density15
Number of external pieces44
Level of complexity24
Related polytopes
ArmySemi-uniform handip
DualHendecagrammic-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, Small hendecagrammic-grand hendecagrammic duoprism, Hendecagrammic-great 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 hendecagrammic-grand hendecagrammic duoprism, also known as the 11/3-11/5 duoprism, is a uniform duoprism that consists of 11 hendecagrammic prisms and 11 grand hendecagrammic prisms, with 2 of each at each vertex.

The name can also refer to the small hendecagrammic-grand hendecagrammic duoprism, the great hendecagrammic-grand hendecagrammic duoprism, or the grand hendecagrammic duoprism.

## Coordinates

The vertex coordinates of a hendecagrammic-grand hendecagrammic duoprism, centered at the origin and with edge length 4sin(3π/11)sin(5π/11), are given by:

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

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