# Great hendecagrammic duoprism

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Great hendecagrammic duoprism
Rank4
TypeUniform
Notation
Coxeter diagramx11/4o x11/4o ()
Elements
Cells22 great hendecagrammic prisms
Faces121 squares, 22 great hendecagrams
Edges242
Vertices121
Vertex figureTetragonal disphenoid, edge lengths 2cos(4π/11) (bases) and 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {2}}{2\sin {\frac {4\pi }{11}}}}\approx 0.77735}$
Inradius${\displaystyle {\frac {1}{2\tan {\frac {4\pi }{11}}}}\approx 0.22834}$
Hypervolume${\displaystyle {\frac {121}{16\tan ^{2}{\frac {4\pi }{11}}}}\approx 1.57724}$
Dichoral anglesGishenp–4–gishenp: 90°
Gishenp–11/4–gishenp: ${\displaystyle {\frac {3\pi }{11}}\approx 49.09091^{\circ }}$
Central density16
Number of external pieces44
Level of complexity12
Related polytopes
ArmyHandip
DualGreat hendecagrammic duotegum
ConjugatesHendecagonal duoprism, Small hendecagrammic duoprism, Hendecagrammic duoprism, Grand hendecagrammic duoprism
Abstract & topological properties
Flag count2904
Euler characteristic0
OrientableYes
Properties
SymmetryI2(11)≀S2, order 968
ConvexNo
NatureTame

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

## Vertex coordinates

The coordinates of a great hendecagrammic duoprism, centered at the origin and with edge length 2sin(4π/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.