Great heptagrammic-hendecagonal duoprism

Great heptagrammic-hendecagonal duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Coxeter diagram	x7/3o x11o ()
Elements
Cells	11 great heptagrammic prisms, 7 hendecagonal prisms
Faces	77 squares, 11 great heptagrams, 7 hendecagons
Edges	77+77
Vertices	77
Vertex figure	Digonal disphenoid, edge lengths 2cos(3π/7) (base 1), 2cos(π/11) (base 2), √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {{\frac {1}{4\sin ^{2}{\frac {3\pi }{7}}}}+{\frac {1}{4\sin ^{2}{\frac {\pi }{11}}}}}}\approx 1.84735$
Hypervolume	${\frac {77}{16\tan {\frac {3\pi }{7}}\tan {\frac {\pi }{11}}}}\approx 3.74088$
Dichoral angles	Giship–7/3–giship: ${\frac {9\pi }{11}}\approx 147.27273^{\circ }$
	Giship–4–henp: 90°
	Henp–11–henp: ${\frac {\pi }{7}}\approx 25.71429^{\circ }$
Central density	3
Number of external pieces	25
Level of complexity	12
Related polytopes
Army	Semi-uniform hehendip
Dual	Great heptagrammic-hendecagonal duotegum
Conjugates	Heptagonal-hendecagonal duoprism, Heptagonal-small hendecagrammic duoprism, Heptagonal-hendecagrammic duoprism, Heptagonal-great hendecagrammic duoprism, Heptagonal-grand hendecagrammic duoprism, Heptagrammic-hendecagonal duoprism, Heptagrammic-small hendecagrammic duoprism, Heptagrammic-hendecagrammic duoprism, Heptagrammic-great hendecagrammic duoprism, Heptagrammic-grand hendecagrammic duoprism, Great heptagrammic-small hendecagrammic duoprism, Great heptagrammic-hendecagrammic duoprism, Great heptagrammic-great hendecagrammic duoprism, Great heptagrammic-grand hendecagrammic duoprism
Abstract & topological properties
Flag count	1848
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	I2(7)×I2(11), order 308
Convex	No
Nature	Tame

The great heptagrammic-hendecagonal duoprism, also known as the 7/3-11 duoprism, is a uniform duoprism that consists of 11 great heptagrammic prisms and 7 hendecagonal prisms, with 2 of each at each vertex.

Vertex coordinates

The coordinates of a great heptagrammic-hendecagonal duoprism, centered at the origin and with edge length 4sin(3π/7)sin(π/11), are given by:

• $\left(2\sin {\frac {\pi }{11}},\,0,\,2\sin {\frac {3\pi }{7}},\,0\right)$,
• $\left(2\sin {\frac {\pi }{11}},\,0,\,2\sin {\frac {3\pi }{7}}\cos \left({\frac {k\pi }{11}}\right),\,\pm 2\sin {\frac {3\pi }{7}}\sin \left({\frac {k\pi }{11}}\right)\right)$,
• $\left(2\sin {\frac {\pi }{11}}\cos \left({\frac {j\pi }{7}}\right),\,\pm 2\sin {\frac {\pi }{11}}\sin \left({\frac {j\pi }{7}}\right),\,2\sin {\frac {3\pi }{7}},\,0\right)$,
• $\left(2\sin {\frac {\pi }{11}}\cos \left({\frac {j\pi }{7}}\right),\,\pm 2\sin {\frac {\pi }{11}}\sin \left({\frac {j\pi }{7}}\right),\,2\sin {\frac {3\pi }{7}}\cos \left({\frac {k\pi }{11}}\right),\,\pm 2\sin {\frac {3\pi }{7}}\sin \left({\frac {k\pi }{11}}\right)\right)$,

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

External links

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

• Klitzing, Richard. "nd-mb-dip".