Hendecagonal-great hendecagrammic duoprism

Hendecagonal-great hendecagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Coxeter diagram	x11o x11/4o ()
Elements
Cells	11 hendecagonal prisms, 11 great hendecagrammic prisms
Faces	121 squares, 11 hendecagons, 11 great hendecagrams
Edges	121+121
Vertices	121
Vertex figure	Digonal disphenoid, edge lengths 2cos(π/11) (base 1), 2cos(4π/11) (base 2), √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {{\frac {1}{4\sin ^{2}{\frac {\pi }{11}}}}+{\frac {1}{4\sin ^{2}{\frac {4\pi }{11}}}}}}\approx 1.85791$
Hypervolume	${\frac {121}{16\tan {\frac {\pi }{11}}\tan {\frac {4\pi }{11}}}}\approx 11.76215$
Dichoral angles	Gishenp–11/4–gishenp: ${\frac {9\pi }{11}}\approx 147.27273^{\circ }$
	Henp–4–gishenp: 90°
	Henp–11–henp: ${\frac {3\pi }{11}}\approx 49.09091^{\circ }$
Central density	4
Number of external pieces	33
Level of complexity	12
Related polytopes
Army	Semi-uniform handip
Dual	Hendecagonal-great hendecagrammic duotegum
Conjugates	Hendecagonal-small hendecagrammic duoprism, Hendecagonal-hendecagrammic duoprism, Hendecagonal-grand hendecagrammic duoprism, Small hendecagrammic-hendecagrammic duoprism, Small hendecagrammic-great hendecagrammic duoprism, Small hendecagrammic-grand hendecagrammic duoprism, Hendecagrammic-great hendecagrammic duoprism, Hendecagrammic-grand hendecagrammic duoprism, Great hendecagrammic-grand hendecagrammic duoprism
Abstract & topological properties
Flag count	2904
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(11)×I2(11), order 484
Convex	No
Nature	Tame

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

Vertex coordinates

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

• $\left(2\sin {\frac {\pi }{11}},\,0,\,2\sin {\frac {4\pi }{11}},\,0\right)$,
• $\left(2\sin {\frac {\pi }{11}},\,0,\,2\sin {\frac {4\pi }{11}}\cos \left({\frac {k\pi }{11}}\right),\,\pm 2\sin {\frac {4\pi }{11}}\sin \left({\frac {k\pi }{11}}\right)\right)$,
• $\left(2\sin {\frac {\pi }{11}}\cos \left({\frac {j\pi }{11}}\right),\,\pm 2\sin {\frac {\pi }{11}}\sin \left({\frac {j\pi }{11}}\right),\,2\sin {\frac {4\pi }{11}},\,0\right)$,
• $\left(2\sin {\frac {\pi }{11}}\cos \left({\frac {j\pi }{11}}\right),\,\pm 2\sin {\frac {\pi }{11}}\sin \left({\frac {j\pi }{11}}\right),\,2\sin {\frac {4\pi }{11}}\cos \left({\frac {k\pi }{11}}\right),\,\pm 2\sin {\frac {4\pi }{11}}\sin \left({\frac {k\pi }{11}}\right)\right)$,

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

External links

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

• Klitzing, Richard. "nd-mb-dip".