Grand hendecagrammic duoprism

Grand hendecagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Coxeter diagram	x11/5o x11/5o ()
Elements
Cells	22 grand hendecagrammic prisms
Faces	121 squares, 22 grand hendecagrams
Edges	242
Vertices	121
Vertex figure	Tetragonal disphenoid, edge lengths 2cos(5π/11) (bases) and √2 (sides)
Measures (edge length 1)
Circumradius	$\frac{\sqrt2}{2\sin\frac{5\pi}{11}} ≈ 0.71438$
Inradius	$\frac{1}{2\tan\frac{5\pi}{11}} ≈ 0.07189$
Hypervolume	$\frac{121}{16\tan^2\frac{5\pi}{11}} ≈ 0.15633$
Dichoral angles	Gashenp–4–gashenp: 90°
	Gashenp–11/5–gashenp: $\frac{\pi}{11} ≈ 16.36364°$
Central density	25
Number of external pieces	44
Level of complexity	12
Related polytopes
Army	Handip
Dual	Grand hendecagrammic duotegum
Conjugates	Hendecagonal duoprism, Small hendecagrammic duoprism, Hendecagrammic duoprism, Great hendecagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(11)≀S2, order 968
Convex	No
Nature	Tame

The grand hendecagrammic duoprism, also known as the grand hendecagrammic-grand hendecagrammic duoprism, the 11/5 duoprism or the 11/5-11/5 duoprism, is a noble uniform duoprism that consists of 22 grand hendecagrammic prisms, with 4 meeting at each vertex.

Vertex coordinates

The vertex coordinates of a grand hendecagrammic duoprism, centered at the origin and with edge length 2sin(5π/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".