# Hendecagonal duoprism

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Hendecagonal duoprism
Rank4
TypeUniform
Notation
Bowers style acronymHandip
Coxeter diagramx11o x11o ()
Elements
Cells22 hendecagonal prisms
Faces121 squares, 22 hendecagons
Edges242
Vertices121
Vertex figureTetragonal disphenoid, edge lengths 2cos(π/11) (bases) and 2 (sides)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {2}}{2\sin {\frac {\pi }{11}}}}\approx 2.50982}$
Inradius${\displaystyle {\frac {1}{2\tan {\frac {\pi }{11}}}}\approx 1.70284}$
Hypervolume${\displaystyle {\frac {121}{16\tan ^{2}{\frac {\pi }{11}}}}\approx 87.71521}$
Dichoral angleHenp–11–henp: ${\displaystyle {\frac {9\pi }{11}}\approx 147.27273^{\circ }}$
Henp–4–henp: 90°
Central density1
Number of external pieces22
Level of complexity3
Related polytopes
ArmyHandip
RegimentHandip
DualHendecagonal duotegum
ConjugatesSmall hendecagrammic duoprism,
Hendecagrammic duoprism,
Great hendecagrammic duoprism,
Grand hendecagrammic duoprism
Abstract & topological properties
Flag count2904
Euler characteristic0
OrientableYes
Properties
SymmetryI2(11)≀S2, order 968
Flag orbits3
ConvexYes
NatureTame

The hendecagonal duoprism or handip, also known as the hendecagonal-hendecagonal duoprism, the 11 duoprism or the 11-11 duoprism, is a noble uniform duoprism that consists of 22 hendecagonal prisms, with 4 joining at each vertex. It is also the 22-10 gyrochoron. It is the first in an infinite family of isogonal hendecagonal dihedral swirlchora and also the first in an infinite family of isochoric hendecagonal hosohedral swirlchora.

## Vertex coordinates

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

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

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