# Heptagonal-hendecagrammic duoprism

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.

Heptagonal-hendecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx7o x11/3o
SymmetryI2(7)×I2(11), order 308
ArmySemi-uniform hehendip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(π/7) (base 1), 2cos(3π/11) (base 2), 2 (sides)
Cells11 heptagonal prisms, 7 hendecagrammic prisms
Faces77 squares, 11 heptagons, 7 hendecagrams
Edges77+77
Vertices77
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 anglesHep–7–hep: 5π/11 ≈ 81.81818°
11/3p–11/3–11/3p: 5π/7 ≈ 128.57143°
Hep–4–11/3p: 90°
Central density3
Related polytopes
DualHeptagonal-hendecagrammic duotegum
ConjugatesHeptagonal-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
ConvexNo
OrientableYes
NatureTame

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)).