Hendecagrammic duoprism

Hendecagrammic duoprism
Rank4
TypeUniform
Notation
Coxeter diagramx11/3o x11/3o ()
Elements
Cells22 hendecagrammic prisms
Faces121 squares, 22 hendecagrams
Edges242
Vertices121
Vertex figureTetragonal disphenoid, edge lengths 2cos(3π/11) (bases) and 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {2}}{2\sin {\frac {3\pi }{11}}}}\approx 0.93564}$
Inradius${\displaystyle {\frac {1}{2\tan {\frac {3\pi }{11}}}}\approx 0.43325}$
Hypervolume${\displaystyle {\frac {121}{16\tan ^{2}{\frac {3\pi }{11}}}}\approx 5.67816}$
Dichoral anglesShenp–4–shenp: 90°
Shenp–11/3–shenp: ${\displaystyle {\frac {5\pi }{11}}\approx 81.81818^{\circ }}$
Central density9
Number of external pieces44
Level of complexity12
Related polytopes
ArmyHandip
DualHendecagrammic duotegum
ConjugatesHendecagonal duoprism, Small hendecagrammic duoprism, Great hendecagrammic duoprism, Grand hendecagrammic duoprism
Abstract & topological properties
Flag count2904
Euler characteristic0
OrientableYes
Properties
SymmetryI2(11)≀S2, order 968
ConvexNo
NatureTame

The hendecagrammic duoprism, also known as the hendecagrammic-hendecagrammic duoprism, the 11/3 duoprism or the 11/3-11/3 duoprism, is a noble uniform duoprism that consists of 22 hendecagrammic prisms, with 4 meeting at each vertex.

Vertex coordinates

The coordinates of a hendecagrammic duoprism, centered at the origin and with edge length 2sin(3π/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.