Heptagonal-hendecagrammic duoprism

Heptagonal-hendecagrammic duoprism
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Info
Coxeter diagram	x7o x11/3o
Symmetry	I2(7)×I2(11), order 308
Army	Semi-uniform hehendip
Elements
Vertex figure	Digonal disphenoid, edge lengths 2cos(π/7) (base 1), 2cos(3π/11) (base 2), √2 (sides)
Cells	11 heptagonal prisms, 7 hendecagrammic prisms
Faces	77 squares, 11 heptagons, 7 hendecagrams
Edges	77+77
Vertices	77
Measures (edge length 1)
Circumradius	$\sqrt{\frac{1}{4\sin^2\frac{\pi}{7}}+\frac{1}{4\sin^2\frac{3\pi}{11}}}≈1.32879$
Hypervolume	$\frac{77}{16\tan\frac{\pi}{7}\tan\frac{3\pi}{11}}≈8.65921$
Dichoral angles	Hep–7–hep: 5π/11 ≈ 81.81818°
	11/3p–11/3–11/3p: 5π/7 ≈ 128.57143°
	Hep–4–11/3p: 90°
Central density	3
Related polytopes
Dual	Heptagonal-hendecagrammic duotegum
Conjugates	Heptagonal-hendecagonal duoprism, Heptagonal-small 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-hendecagonal duoprism, Great heptagrammic-small hendecagrammic duoprism, Great heptagrammic-hendecagrammic duoprism, Great heptagrammic-great hendecagrammic duoprism, Great heptagrammic-grand hendecagrammic duoprism
Properties
Convex	No
Orientable	Yes
Nature	Tame

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

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

Vertex coordinates

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

• (2sin(3π/11), 0, 1, 0),
• (2sin(3π/11), 0, 2sin(π/7)cos(2π/11), ±2sin(π/7)sin(2π/11)),
• (2sin(3π/11), 0, 2sin(π/7)cos(4π/11), ±2sin(π/7)sin(4π/11)),
• (2sin(3π/11), 0, 2sin(π/7)cos(6π/11), ±2sin(π/7)sin(6π/11)),
• (2sin(3π/11), 0, 2sin(π/7)cos(8π/11), ±2sin(π/7)sin(8π/11)),
• (2sin(3π/11), 0, 2sin(π/7)cos(10π/11), ±2sin(π/7)sin(10π/11)),
• (2sin(3π/11)cos(2π/7), ±2sin(3π/11)sin(2π/7), 1, 0),
• (2sin(3π/11)cos(2π/7), ±2sin(3π/11)sin(2π/7), 2sin(π/7)cos(2π/11), ±2sin(π/7)sin(2π/11)),
• (2sin(3π/11)cos(2π/7), ±2sin(3π/11)sin(2π/7), 2sin(π/7)cos(4π/11), ±2sin(π/7)sin(4π/11)),
• (2sin(3π/11)cos(2π/7), ±2sin(3π/11)sin(2π/7), 2sin(π/7)cos(6π/11), ±2sin(π/7)sin(6π/11)),
• (2sin(3π/11)cos(2π/7), ±2sin(3π/11)sin(2π/7), 2sin(π/7)cos(8π/11), ±2sin(π/7)sin(8π/11)),
• (2sin(3π/11)cos(2π/7), ±2sin(3π/11)sin(2π/7), 2sin(π/7)cos(10π/11), ±2sin(π/7)sin(10π/11)),
• (2sin(3π/11)cos(4π/7), ±2sin(3π/11)sin(4π/7), 1, 0),
• (2sin(3π/11)cos(4π/7), ±2sin(3π/11)sin(4π/7), 2sin(π/7)cos(2π/11), ±2sin(π/7)sin(2π/11)),
• (2sin(3π/11)cos(4π/7), ±2sin(3π/11)sin(4π/7), 2sin(π/7)cos(4π/11), ±2sin(π/7)sin(4π/11)),
• (2sin(3π/11)cos(4π/7), ±2sin(3π/11)sin(4π/7), 2sin(π/7)cos(6π/11), ±2sin(π/7)sin(6π/11)),
• (2sin(3π/11)cos(4π/7), ±2sin(3π/11)sin(4π/7), 2sin(π/7)cos(8π/11), ±2sin(π/7)sin(8π/11)),
• (2sin(3π/11)cos(4π/7), ±2sin(3π/11)sin(4π/7), 2sin(π/7)cos(10π/11), ±2sin(π/7)sin(10π/11)),
• (2sin(3π/11)cos(6π/7), ±2sin(3π/11)sin(6π/7), 1, 0),
• (2sin(3π/11)cos(6π/7), ±2sin(3π/11)sin(6π/7), 2sin(π/7)cos(2π/11), ±2sin(π/7)sin(2π/11)),
• (2sin(3π/11)cos(6π/7), ±2sin(3π/11)sin(6π/7), 2sin(π/7)cos(4π/11), ±2sin(π/7)sin(4π/11)),
• (2sin(3π/11)cos(6π/7), ±2sin(3π/11)sin(6π/7), 2sin(π/7)cos(6π/11), ±2sin(π/7)sin(6π/11)),
• (2sin(3π/11)cos(6π/7), ±2sin(3π/11)sin(6π/7), 2sin(π/7)cos(8π/11), ±2sin(π/7)sin(8π/11)),
• (2sin(3π/11)cos(6π/7), ±2sin(3π/11)sin(6π/7), 2sin(π/7)cos(10π/11), ±2sin(π/7)sin(10π/11)).

External links

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