Enneagrammic-hendecagonal duoprism

Enneagrammic-hendecagonal duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Coxeter diagram	x9/2o x11o ()
Elements
Cells	11 enneagrammic prisms, 9 hendecagonal prisms
Faces	99 squares, 11 enneagrams, 9 hendecagons
Edges	99+99
Vertices	99
Vertex figure	Digonal disphenoid, edge lengths 2cos(2π/9) (base 1), 2cos(π/11) (base 2), √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {{\frac {1}{4\sin ^{2}{\frac {2\pi }{9}}}}+{\frac {1}{4\sin ^{2}{\frac {\pi }{11}}}}}}\approx 1.93772$
Hypervolume	${\frac {99}{16\tan {\frac {2\pi }{9}}\tan {\frac {\pi }{11}}}}\approx 25.11345$
Dichoral angles	Step–9/2–step: ${\frac {9\pi }{11}}\approx 147.27273^{\circ }$
	Henp–11–henp: 100°
	Step–4–henp: 90°
Central density	2
Number of external pieces	29
Level of complexity	12
Related polytopes
Army	Semi-uniform ehendip
Dual	Enneagrammic-hendecagonal duotegum
Conjugates	Enneagonal-hendecagonal duoprism, Enneagonal-small hendecagrammic duoprism, Enneagonal-hendecagrammic duoprism, Enneagonal-great hendecagrammic duoprism, Enneagonal-grand hendecagrammic duoprism, Enneagrammic-small hendecagrammic duoprism, Enneagrammic-hendecagrammic duoprism, Enneagrammic-great hendecagrammic duoprism, Enneagrammic-grand hendecagrammic duoprism, Great enneagrammic-hendecagonal duoprism, Great enneagrammic-small hendecagrammic duoprism, Great enneagrammic-hendecagrammic duoprism, Great enneagrammic-great hendecagrammic duoprism, Great enneagrammic-grand hendecagrammic duoprism
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(9)×I2(11), order 396
Convex	No
Nature	Tame

The enneagrammic-hendecagonal duoprism, also known as the 9/2-11 duoprism, is a uniform duoprism that consists of 11 enneagrammic prisms and 9 hendecagonal prisms, with 2 of each at each vertex.

The name can also refer to the great enneagrammic-hendecagonal duoprism.

Vertex coordinates

The coordinates of an enneagrammic-hendecagonal duoprism, centered at the origin and with edge length 4sin(2π/9)sin(π/11), are given by:

• $\left(2\sin {\frac {\pi }{11}},\,0,\,2\sin {\frac {2\pi }{9}},\,0\right)$,
• $\left(2\sin {\frac {\pi }{11}},\,0,\,2\sin {\frac {2\pi }{9}}\cos \left({\frac {k\pi }{11}}\right),\,\pm 2\sin {\frac {2\pi }{9}}\sin \left({\frac {k\pi }{11}}\right)\right)$,
• $\left(2\sin {\frac {\pi }{11}}\cos \left({\frac {j\pi }{9}}\right),\,\pm 2\sin {\frac {\pi }{11}}\sin \left({\frac {j\pi }{9}}\right),\,2\sin {\frac {2\pi }{9}},\,0\right)$,
• $\left(2\sin {\frac {\pi }{11}}\cos \left({\frac {j\pi }{9}}\right),\,\pm 2\sin {\frac {\pi }{11}}\sin \left({\frac {j\pi }{9}}\right),\,2\sin {\frac {2\pi }{9}}\cos \left({\frac {k\pi }{11}}\right),\,\pm 2\sin {\frac {2\pi }{9}}\sin \left({\frac {k\pi }{11}}\right)\right)$,
• $\left(-\sin {\frac {\pi }{11}},\,\pm {\sqrt {3}}\sin {\frac {\pi }{11}},\,2\sin {\frac {2\pi }{9}},\,0\right)$,
• $\left(-\sin {\frac {\pi }{11}},\,\pm {\sqrt {3}}\sin {\frac {\pi }{11}},\,2\sin {\frac {2\pi }{9}}\cos \left({\frac {k\pi }{11}}\right),\,\pm 2\sin {\frac {2\pi }{9}}\sin \left({\frac {k\pi }{11}}\right)\right)$,

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

External links

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

• Klitzing, Richard. "nd-mb-dip".