Small hendecagrammic-great hendecagrammic duoprism

Small hendecagrammic-great hendecagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Coxeter diagram	x11/2o x11/4o ()
Elements
Cells	11 small hendecagrammic prisms, 11 great hendecagrammic prisms
Faces	121 squares, 11 small hendecagrams, 11 great hendecagrams
Edges	121+121
Vertices	121
Vertex figure	Digonal disphenoid, edge lengths 2cos(2π/11) (base 1), 2cos(4π/11) (base 2), √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {4\cos ^{2}{\frac {2\pi }{11}}+1}{4\sin ^{2}{\frac {4\pi }{11}}}}}\approx 1.07585$
Hypervolume	$121{\frac {1-\tan ^{2}{\frac {2\pi }{11}}}{32\tan ^{2}{\frac {2\pi }{11}}}}\approx 5.37403$
Dichoral angles	Gishenp–11/4–gishenp: ${\frac {7\pi }{11}}\approx 114.54545^{\circ }$
	Sishenp–4–gishenp: 90°
	Sishenp–11/2–sishenp: ${\frac {3\pi }{11}}\approx 49.09091^{\circ }$
Central density	8
Number of external pieces	44
Level of complexity	24
Related polytopes
Army	Semi-uniform handip
Dual	Small hendecagrammic-great hendecagrammic duotegum
Conjugates	Hendecagonal-small hendecagrammic duoprism, Hendecagonal-hendecagrammic duoprism, Hendecagonal-great hendecagrammic duoprism, Hendecagonal-grand hendecagrammic duoprism, Small hendecagrammic-hendecagrammic duoprism, Small hendecagrammic-grand hendecagrammic duoprism, Hendecagrammic-great hendecagrammic duoprism, Hendecagrammic-grand hendecagrammic duoprism, Great hendecagrammic-grand hendecagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(11)×I2(11), order 484
Convex	No
Nature	Tame

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

The vertex coordinates of a small hendecagrammic-grand hendecagrammic duoprism, centered at the origin and with edge length 2sin(4π/11), are given by:

• $\left(2\cos {\frac {2\pi }{11}},\,0,\,1,\,0\right),$
• $\left(2\cos {\frac {2\pi }{11}},\,0,\,\cos \left({\frac {k\pi }{11}}\right),\,\pm \sin \left({\frac {k\pi }{11}}\right)\right),$
• $\left(2\cos {\frac {2\pi }{11}}\cos \left({\frac {j\pi }{11}}\right),\,\pm 2\cos {\frac {2\pi }{11}}\sin \left({\frac {j\pi }{11}}\right),\,1,\,0\right),$
• $\left(2\cos {\frac {2\pi }{11}}\cos \left({\frac {j\pi }{11}}\right),\,\pm 2\cos {\frac {2\pi }{11}}\sin \left({\frac {j\pi }{11}}\right),\,\cos \left({\frac {k\pi }{11}}\right),\,\pm \sin \left({\frac {k\pi }{11}}\right)\right),$

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

External links

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

• Klitzing, Richard. "nd-mb-dip".