Small hendecagrammic duoprism

Small hendecagrammic duoprism
Rank4
TypeUniform
Notation
Coxeter diagramx11/2o x11/2o ()
Elements
Cells22 small hendecagrammic prisms
Faces121 squares, 22 small hendecagrams
Edges242
Vertices121
Vertex figureTetragonal disphenoid, edge lengths 2cos(2π/11) (bases) and 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {2}}{2\sin {\frac {2\pi }{11}}}}\approx 1.30790}$
Inradius${\displaystyle {\frac {1}{2\tan {\frac {2\pi }{11}}}}\approx 0.77802}$
Hypervolume${\displaystyle {\frac {121}{16\tan ^{2}{\frac {2\pi }{11}}}}\approx 18.31056}$
Dichoral anglesSishenp–11/2–sishenp: ${\displaystyle {\frac {7\pi }{11}}\approx 114.54545^{\circ }}$
Sishenp–4–sishenp: 90°
Central density4
Number of external pieces44
Level of complexity12
Related polytopes
ArmyHandip
DualSmall hendecagrammic duotegum
ConjugatesHendecagonal duoprism, Hendecagrammic duoprism, Great hendecagrammic duoprism, Grand hendecagrammic duoprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryI2(11)≀S2, order 968
ConvexNo
NatureTame

The small hendecagrammic duoprism, also known as the small hendecagrammic-small hendecagrammic duoprism, the 11/2 duoprism or the 11/2-11/2 duoprism, is a noble uniform duoprism that consists of 22 small hendecagrammic prisms, with 4 meeting at each vertex.

Vertex coordinates

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