# Hendecagonal duoprism

Hendecagonal duoprism Rank4
TypeUniform
SpaceSpherical
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$\frac{\sqrt2}{2\sin\frac{\pi}{11}} ≈ 2.50982$ Inradius$\frac{1}{2\tan\frac{\pi}{11}} ≈ 1.70284$ Hypervolume$\frac{121}{16\tan^2\frac{\pi}{11}} ≈ 87.71521$ Dichoral anglesHenp–11–henp: $\frac{9\pi}{11} ≈ 147.27273°$ 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
Euler characteristic0
OrientableYes
Properties
SymmetryI2(11)≀S2, order 968
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:

• $\left(1,0,1,0\right),$ • $\left(1,0,\cos\left(\frac{j\pi}{11}\right),±\sin\left(\frac{j\pi}{11}\right)\right),$ • $\left(\cos\left(\frac{k\pi}{11}\right),±\sin\left(\frac{k\pi}{11}\right),1,0\right),$ • $\left(\cos\left(\frac{k\pi}{11}\right),±\sin\left(\frac{k\pi}{11}\right),\cos\left(\frac{j\pi}{11}\right),±\sin\left(\frac{j\pi}{11}\right)\right),$ where j, k = 2, 4, 6, 8, 10.