# Grand hendecagrammic duoprism

Grand hendecagrammic duoprism
Rank4
TypeUniform
Notation
Coxeter diagramx11/5o x11/5o ()
Elements
Cells22 grand hendecagrammic prisms
Faces121 squares, 22 grand hendecagrams
Edges242
Vertices121
Vertex figureTetragonal disphenoid, edge lengths 2cos(5π/11) (bases) and 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {2}}{2\sin {\frac {5\pi }{11}}}}\approx 0.71438}$
Inradius${\displaystyle {\frac {1}{2\tan {\frac {5\pi }{11}}}}\approx 0.07189}$
Hypervolume${\displaystyle {\frac {121}{16\tan ^{2}{\frac {5\pi }{11}}}}\approx 0.15633}$
Dichoral anglesGashenp–4–gashenp: 90°
Gashenp–11/5–gashenp: ${\displaystyle {\frac {\pi }{11}}\approx 16.36364^{\circ }}$
Central density25
Number of external pieces44
Level of complexity12
Related polytopes
ArmyHandip
DualGrand hendecagrammic duotegum
ConjugatesHendecagonal duoprism, Small hendecagrammic duoprism, Hendecagrammic duoprism, Great hendecagrammic duoprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(11)≀S2, order 968
ConvexNo
NatureTame

The grand hendecagrammic duoprism, also known as the grand hendecagrammic-grand hendecagrammic duoprism, the 11/5 duoprism or the 11/5-11/5 duoprism, is a noble uniform duoprism that consists of 22 grand hendecagrammic prisms, with 4 meeting at each vertex.

## Vertex coordinates

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

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

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