Heptagrammic-hendecagrammic duoprism

Heptagrammic-hendecagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Notation
Coxeter diagram	x7/2o x11/3o ()
Elements
Cells	11 heptagrammic prisms, 7 hendecagrammic prisms
Faces	77 squares, 11 heptagrams, 7 hendecagrams
Edges	77+77
Vertices	77
Vertex figure	Digonal disphenoid, edge lengths 2cos(2π/7) (base 1), 2cos(3π/11) (base 2), √2 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {{\frac {1}{4\sin ^{2}{\frac {2\pi }{7}}}}+{\frac {1}{4\sin ^{2}{\frac {3\pi }{11}}}}}}\approx 0.92016$
Hypervolume	${\frac {77}{16\tan {\frac {2\pi }{7}}\tan {\frac {3\pi }{11}}}}\approx 3.32551$
Dichoral angles	Ship–4–shenp: 90°
	Ship–7/2–ship: ${\frac {5\pi }{11}}\approx 81.81818^{\circ }$
	Shenp–11/3–shenp: ${\frac {3\pi }{7}}\approx 77.14286^{\circ }$
Central density	6
Number of external pieces	36
Level of complexity	24
Related polytopes
Army	Semi-uniform hehendip
Dual	Heptagrammic-hendecagrammic 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-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 heptagrammic-hendecagrammic duoprism, also known as the 7/2-11/3 duoprism, is a uniform duoprism that consists of 11 heptagrammic prisms and 7 hendecagrammic prisms, with 2 of each at each vertex.

The name can also refer to the heptagrammic-small hendecagrammic duoprism, the heptagrammic-great hendecagrammic duoprism, the heptagrammic-grand hendecagrammic duoprism, the great heptagrammic-small hendecagrammic duoprism, the great heptagrammic-hendecagrammic duoprism, the great heptagrammic-great hendecagrammic duoprism, or the great heptagrammic-grand hendecagrammic duoprism.

Vertex coordinates

The coordinates of a heptagrammic-hendecagrammic duoprism, centered at the origin and with edge length 4sin(2π/7)sin(3π/11), are given by:

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

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

External links

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

• Klitzing, Richard. "nd-mb-dip".