# Enneagonal-hendecagonal duoprism

(Redirected from Ehendip)
Enneagonal-hendecagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymEhendip
Info
Coxeter diagramx9o x11o
SymmetryI2(9)×I2(11), order 396
ArmyEhendip
RegimentEhendip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(π/9) (base 1), 2cos(π/11) (base 2), and 2 (sides)
Cells11 enneagonal prisms, 9 hendecagonal prisms
Faces99 squares, 11 enneagons, 9 hendecagons
Edges99+99
Vertices99
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{1}{4\sin^2\frac\pi9}+\frac{1}{4\sin^2\frac{\pi}{11}}} ≈ 2.29931}$
Hypervolume${\displaystyle \frac{99}{16\tan\frac\pi9\tan\frac{\pi}{11}} ≈ 57.89674}$
Dichoral anglesEp–9–ep: ${\displaystyle \frac{9\pi}{11} ≈ 147.27273°}$
Henp–11–henp: 140°
Ep–4–henp: 90°
Central density1
Euler characteristic0
Number of pieces20
Level of complexity6
Related polytopes
DualEnneagonal-hendecagonal duotegum
ConjugatesEnneagonal-small hendecagrammic duoprism, Enneagonal-hendecagrammic duoprism, Enneagonal-great hendecagrammic duoprism, Enneagonal-grand hendecagrammic duoprism, Enneagrammic-hendecagonal duoprism, Enneagrammic-small hendecagrammic duoprism, Enneagrammic-hendecagrammic duoprism, Enneagrammic-great hendecagrammic duoprism, Enneagrammic-grand hendecagrammic duoprism, Great enneagrammic-hendecagonal duoprism, Great enneagrammic-small hendecagrammic duoprism, Great enneagrammic-hendecagrammic duoprism, Great enneagrammic-great hendecagrammic duoprism, Great enneagrammic-grand hendecagrammic duoprism
Properties
ConvexYes
OrientableYes
NatureTame

The enneagonal-hendecagonal duoprism or ehendip, also known as the 9-11 duoprism, is a uniform duoprism that consists of 9 hendecagonal prisms and 11 enneagonal prisms, with two ofe each joining at each vertex.

## Vertex coordinates

The coordinates of an enneagonal-hendecagonal duoprism, centered at the origin and with edge length 4sin(π/9)sin(π/11), are given by:

• (2sin(π/11), 0, 2sin(π/9), 0),
• (2sin(π/11), 0, 2sin(π/9)cos(2π/11), ±2sin(π/9)sin(2π/11)),
• (2sin(π/11), 0, 2sin(π/9)cos(4π/11), ±2sin(π/9)sin(4π/11)),
• (2sin(π/11), 0, 2sin(π/9)cos(6π/11), ±2sin(π/9)sin(6π/11)),
• (2sin(π/11), 0, 2sin(π/9)cos(8π/11), ±2sin(π/9)sin(8π/11)),
• (2sin(π/11), 0, 2sin(π/9)cos(10π/11), ±2sin(π/9)sin(10π/11)),
• (2sin(π/11)cos(2π/9), ±2sin(π/11)sin(2π/9), 2sin(π/9), 0),
• (2sin(π/11)cos(2π/9), ±2sin(π/11)sin(2π/9), 2sin(π/9)cos(2π/11), ±2sin(π/9)sin(2π/11)),
• (2sin(π/11)cos(2π/9), ±2sin(π/11)sin(2π/9), 2sin(π/9)cos(4π/11), ±2sin(π/9)sin(4π/11)),
• (2sin(π/11)cos(2π/9), ±2sin(π/11)sin(2π/9), 2sin(π/9)cos(6π/11), ±2sin(π/9)sin(6π/11)),
• (2sin(π/11)cos(2π/9), ±2sin(π/11)sin(2π/9), 2sin(π/9)cos(8π/11), ±2sin(π/9)sin(8π/11)),
• (2sin(π/11)cos(2π/9), ±2sin(π/11)sin(2π/9), 2sin(π/9)cos(10π/11), ±2sin(π/9)sin(10π/11)),
• (2sin(π/11)cos(4π/9), ±2sin(π/11)sin(4π/9), 2sin(π/9), 0),
• (2sin(π/11)cos(4π/9), ±2sin(π/11)sin(4π/9), 2sin(π/9)cos(2π/11), ±2sin(π/9)sin(2π/11)),
• (2sin(π/11)cos(4π/9), ±2sin(π/11)sin(4π/9), 2sin(π/9)cos(4π/11), ±2sin(π/9)sin(4π/11)),
• (2sin(π/11)cos(4π/9), ±2sin(π/11)sin(4π/9), 2sin(π/9)cos(6π/11), ±2sin(π/9)sin(6π/11)),
• (2sin(π/11)cos(4π/9), ±2sin(π/11)sin(4π/9), 2sin(π/9)cos(8π/11), ±2sin(π/9)sin(8π/11)),
• (2sin(π/11)cos(4π/9), ±2sin(π/11)sin(4π/9), 2sin(π/9)cos(10π/11), ±2sin(π/9)sin(10π/11)),
• (–sin(π/11), ±sin(π/11)3, 2sin(π/9), 0),
• (–sin(π/11), ±sin(π/11)3, 2sin(π/9)cos(2π/11), ±2sin(π/9)sin(2π/11)),
• (–sin(π/11), ±sin(π/11)3, 2sin(π/9)cos(4π/11), ±2sin(π/9)sin(4π/11)),
• (–sin(π/11), ±sin(π/11)3, 2sin(π/9)cos(6π/11), ±2sin(π/9)sin(6π/11)),
• (–sin(π/11), ±sin(π/11)3, 2sin(π/9)cos(8π/11), ±2sin(π/9)sin(8π/11)),
• (–sin(π/11), ±sin(π/11)3, 2sin(π/9)cos(10π/11), ±2sin(π/9)sin(10π/11)),
• (2sin(π/11)cos(8π/9), ±2sin(π/11)sin(8π/9), 2sin(π/9), 0),
• (2sin(π/11)cos(8π/9), ±2sin(π/11)sin(8π/9), 2sin(π/9)cos(2π/11), ±2sin(π/9)sin(2π/11)),
• (2sin(π/11)cos(8π/9), ±2sin(π/11)sin(8π/9), 2sin(π/9)cos(4π/11), ±2sin(π/9)sin(4π/11)),
• (2sin(π/11)cos(8π/9), ±2sin(π/11)sin(8π/9), 2sin(π/9)cos(6π/11), ±2sin(π/9)sin(6π/11)),
• (2sin(π/11)cos(8π/9), ±2sin(π/11)sin(8π/9), 2sin(π/9)cos(8π/11), ±2sin(π/9)sin(8π/11)),
• (2sin(π/11)cos(8π/9), ±2sin(π/11)sin(8π/9), 2sin(π/9)cos(10π/11), ±2sin(π/9)sin(10π/11)).