# Great heptagrammic-hendecagonal duoprism

(Redirected from 7/3-11 duoprism)
Great heptagrammic-hendecagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx7/3o x11o
SymmetryI2(7)×I2(11), order 308
ArmySemi-uniform hehendip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(3π/7) (base 1), 2cos(π/11) (base 2), 2 (sides)
Cells11 great heptagrammic prisms, 7 hendecagonal prisms
Faces77 squares, 11 great heptagrams, 7 hendecagons
Edges77+77
Vertices77
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{1}{4\sin^2\frac{3\pi}{7}}+\frac{1}{4\sin^2\frac{\pi}{11}}}≈1.84735}$
Hypervolume${\displaystyle \frac{77}{16\tan\frac{3\pi}{7}\tan\frac{\pi}{11}}≈3.74088}$
Dichoral anglesGiship–7/3–giship: 9π/11 ≈ 147.27273°
11p–11–11p: π/7 ≈ 25.71429°
Giship–4–11p: 90°
Central density3
Related polytopes
DualGreat heptagrammic-hendecagonal duotegum
ConjugatesHeptagonal-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
Properties
ConvexNo
OrientableYes
NatureTame

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 meeting 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:

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