Heptagonal-great hendecagrammic duoprism

Heptagonal-great hendecagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Coxeter diagram	x7o x11/4o ()
Elements
Cells	11 heptagonal prisms, 7 great hendecagrammic prisms
Faces	77 squares, 11 heptagons, 7 great hendecagrams
Edges	77+77
Vertices	77
Vertex figure	Digonal disphenoid, edge lengths 2cos(π/7) (base 1), 2cos(4π/11) (base 2), √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {{\frac {1}{4\sin ^{2}{\frac {\pi }{7}}}}+{\frac {1}{4\sin ^{2}{\frac {4\pi }{11}}}}}}\approx 1.27676$
Hypervolume	${\frac {77}{16\tan {\frac {\pi }{7}}\tan {\frac {4\pi }{11}}}}\approx 4.56377$
Dichoral angles	Gishenp–11/4–gishenp: ${\frac {5\pi }{7}}\approx 128.57143^{\circ }$
	Hep–4–gishenp: 90°
	Hep–7–hep: ${\frac {3\pi }{11}}\approx 49.09091^{\circ }$
Central density	4
Number of external pieces	29
Level of complexity	12
Related polytopes
Army	Semi-uniform hehendip
Dual	Heptagonal-great hendecagrammic duotegum
Conjugates	Heptagonal-hendecagonal duoprism, Heptagonal-small hendecagrammic duoprism, Heptagonal-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-hendecagonal 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 heptagonal-great hendecagrammic duoprism, also known as the 7-11/4 duoprism, is a uniform duoprism that consists of 11 heptagonal prisms and 7 great hendecagrammic prisms, with 2 of each at each vertex.

Vertex coordinates

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

• $\left(2\sin {\frac {4\pi }{11}},\,0,\,2\sin {\frac {\pi }{7}},\,0\right)$,
• $\left(2\sin {\frac {4\pi }{11}},\,0,\,2\sin {\frac {\pi }{7}}\cos \left({\frac {k\pi }{11}}\right),\,\pm 2\sin {\frac {\pi }{7}}\sin \left({\frac {k\pi }{11}}\right)\right)$,
• $\left(2\sin {\frac {4\pi }{11}}\cos \left({\frac {j\pi }{7}}\right),\,\pm 2\sin {\frac {4\pi }{11}}\sin \left({\frac {j\pi }{7}}\right),\,2\sin {\frac {\pi }{7}},\,0\right)$,
• $\left(2\sin {\frac {4\pi }{11}}\cos \left({\frac {j\pi }{7}}\right),\,\pm 2\sin {\frac {4\pi }{11}}\sin \left({\frac {j\pi }{7}}\right),\,2\sin {\frac {\pi }{7}}\cos \left({\frac {k\pi }{11}}\right),\,\pm 2\sin {\frac {\pi }{7}}\sin \left({\frac {k\pi }{11}}\right)\right)$,

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

External links

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

• Klitzing, Richard. "nd-mb-dip".