Hendecagonal duoprism

Hendecagonal duoprism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Handip
Coxeter diagram	x11o x11o ()
Elements
Cells	22 hendecagonal prisms
Faces	121 squares, 22 hendecagons
Edges	242
Vertices	121
Vertex figure	Tetragonal 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 angles	Henp–11–henp: $\frac{9\pi}{11} ≈ 147.27273°$
	Henp–4–henp: 90°
Central density	1
Number of external pieces	22
Level of complexity	3
Related polytopes
Army	Handip
Regiment	Handip
Dual	Hendecagonal duotegum
Conjugates	Small hendecagrammic duoprism, Hendecagrammic duoprism, Great hendecagrammic duoprism, Grand hendecagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(11)≀S2, order 968
Convex	Yes
Nature	Tame

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.

External links

• Bowers, Jonathan. "Category A: Duoprisms".

• Klitzing, Richard. "n-n-dip".