# Hendecagonal duoprism

(Redirected from 11-11 duoprism)
Hendecagonal duoprism Rank4
TypeUniform
SpaceSpherical
Bowers style acronymHandip
Info
Coxeter diagramx11o x11o
SymmetryI2(11)≀S2, order 968
ArmyHandip
RegimentHandip
Elements
Vertex figureTetragonal disphenoid, edge lengths 2cos(π/11) (bases) and 2 (sides)
Cells22 hendecagonal prisms
Faces121 squares, 22 hendecagons
Edges242
Vertices121
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
Euler characteristic0
Number of pieces22
Level of complexity3
Related polytopes
DualHendecagonal duotegum
ConjugatesSmall hendecagrammic duoprism, Hendecagrammic duoprism, Great hendecagrammic duoprism, Grand hendecagrammic duoprism
Properties
ConvexYes
OrientableYes
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:

• (1, 0, 1, 0),
• (1, 0, cos(2π/11), ±sin(2π/11)),
• (1, 0, cos(4π/11), ±sin(4π/11)),
• (1, 0, cos(6π/11), ±sin(6π/11)),
• (1, 0, cos(8π/11), ±sin(8π/11)),
• (1, 0, cos(10π/11), ±sin(10π/11)),
• (cos(2π/11), ±sin(2π/11), 1, 0),
• (cos(2π/11), ±sin(2π/11), cos(2π/11), ±sin(2π/11)),
• (cos(2π/11), ±sin(2π/11), cos(4π/11), ±sin(4π/11)),
• (cos(2π/11), ±sin(2π/11), cos(6π/11), ±sin(6π/11)),
• (cos(2π/11), ±sin(2π/11), cos(8π/11), ±sin(8π/11)),
• (cos(2π/11), ±sin(2π/11), cos(10π/11), ±sin(10π/11)),
• (cos(4π/11), ±sin(4π/11), 1, 0),
• (cos(4π/11), ±sin(4π/11), cos(2π/11), ±sin(2π/11)),
• (cos(4π/11), ±sin(4π/11), cos(4π/11), ±sin(4π/11)),
• (cos(4π/11), ±sin(4π/11), cos(6π/11), ±sin(6π/11)),
• (cos(4π/11), ±sin(4π/11), cos(8π/11), ±sin(8π/11)),
• (cos(4π/11), ±sin(4π/11), cos(10π/11), ±sin(10π/11)),
• (cos(6π/11), ±sin(6π/11), 1, 0),
• (cos(6π/11), ±sin(6π/11), cos(2π/11), ±sin(2π/11)),
• (cos(6π/11), ±sin(6π/11), cos(4π/11), ±sin(4π/11)),
• (cos(6π/11), ±sin(6π/11), cos(6π/11), ±sin(6π/11)),
• (cos(6π/11), ±sin(6π/11), cos(8π/11), ±sin(8π/11)),
• (cos(6π/11), ±sin(6π/11), cos(10π/11), ±sin(10π/11)),
• (cos(8π/11), ±sin(8π/11), 1, 0),
• (cos(8π/11), ±sin(8π/11), cos(2π/11), ±sin(2π/11)),
• (cos(8π/11), ±sin(8π/11), cos(4π/11), ±sin(4π/11)),
• (cos(8π/11), ±sin(8π/11), cos(6π/11), ±sin(6π/11)),
• (cos(8π/11), ±sin(8π/11), cos(8π/11), ±sin(8π/11)),
• (cos(8π/11), ±sin(8π/11), cos(10π/11), ±sin(10π/11)),
• (cos(10π/11), ±sin(10π/11), 1, 0),
• (cos(10π/11), ±sin(10π/11), cos(2π/11), ±sin(2π/11)),
• (cos(10π/11), ±sin(10π/11), cos(4π/11), ±sin(4π/11)),
• (cos(10π/11), ±sin(10π/11), cos(6π/11), ±sin(6π/11)),
• (cos(10π/11), ±sin(10π/11), cos(8π/11), ±sin(8π/11)),
• (cos(10π/11), ±sin(10π/11), cos(10π/11), ±sin(10π/11)).