Heptagonal-hendecagonal duoprism

Heptagonal-hendecagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymHehendip
Info
Coxeter diagramx7o x11o
SymmetryI2(7)×I2(11), order 308
ArmyHehendip
RegimentHehendip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(π/7) (base 1), 2cos(π/11) (base 2), and 2 (sides)
Cells11 heptagonal prisms, 7 hendecagonal prisms
Faces77 squares, 11 heptagons, 7 hendecagons
Edges77+77
Vertices77
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{1}{4\sin^2\frac\pi7}+\frac{1}{4\sin^2\frac{\pi}{11}}} ≈ 2.11605}$
Hypervolume${\displaystyle \frac{77}{16\tan\frac\pi7\tan\frac{\pi}{11}} ≈ 34.03392}$
Dichoral anglesHep–7–hep: ${\displaystyle \frac{9\pi}{11} ≈ 147.27273°}$
Henp–11–henp: ${\displaystyle \frac{5\pi}{7} ≈ 128.57143°}$
Hep–4–henp: 90°
Central density1
Euler characteristic0
Number of pieces18
Level of complexity6
Related polytopes
DualHeptagonal-hendecagonal duotegum
ConjugatesHeptagonal-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-hendecagonal duoprism, Great heptagrammic-small hendecagrammic duoprism, Great heptagrammic-hendecagrammic duoprism, Great heptagrammic-great hendecagrammic duoprism, Great heptagrammic-grand hendecagrammic duoprism
Properties
ConvexYes
OrientableYes
NatureTame

The heptagonal-hendecagonal duoprism or hehendip, also known as the 7-11 duoprism, is a uniform duoprism that consists of 7 hendecagonal prisms and 11 heptagonal prisms, with two of each joining at each vertex.

Vertex coordinates

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

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