Small hendecagrammic duoprism

Small hendecagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Coxeter diagram	x11/2o x11/2o ()
Elements
Cells	22 small hendecagrammic prisms
Faces	121 squares, 22 small hendecagrams
Edges	242
Vertices	121
Vertex figure	Tetragonal disphenoid, edge lengths 2cos(2π/11) (bases) and √2 (sides)
Measures (edge length 1)
Circumradius	$\frac{\sqrt2}{2\sin\frac{2\pi}{11}} ≈ 1.30790$
Inradius	$\frac{1}{2\tan\frac{2\pi}{11}} ≈ 0.77802$
Hypervolume	$\frac{121}{16\tan^2\frac{2\pi}{11}} ≈ 18.31056$
Dichoral angles	Sishenp–11/2–sishenp: $\frac{7\pi}{11} ≈ 114.54545°$
	Sishenp–4–sishenp: 90°
Central density	4
Number of external pieces	44
Level of complexity	12
Related polytopes
Army	Handip
Dual	Small hendecagrammic duotegum
Conjugates	Hendecagonal 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	No
Nature	Tame

The small hendecagrammic duoprism, also known as the small hendecagrammic-small hendecagrammic duoprism, the 11/2 duoprism or the 11/2-11/2 duoprism, is a noble uniform duoprism that consists of 22 small hendecagrammic prisms, with 4 meeting at each vertex.

Vertex coordinates

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

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

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

External links

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

• Klitzing, Richard. "nd-mb-dip".