# Small hendecagrammic-grand hendecagrammic duoprism

(Redirected from 11/5-11/2 duoprism)
Small hendecagrammic-grand hendecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx11/2o x11/5o
SymmetryI2(11)×I2(11), order 484
ArmySemi-uniform handip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(2π/11) (base 1), 2cos(5π/11) (base 2), 2 (sides)
Cells11 small hendecagrammic prisms, 11 grand hendecagrammic prisms
Faces11 small hendecagrams, 11 grand hendecagrams, 121 squares
Edges121+121
Vertices121
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{1}{4\sin^2\frac{2\pi}{11}}+\frac{1}{4\sin^2\frac{5\pi}{11}}}≈1.05379}$
Hypervolume${\displaystyle \frac{121}{16\tan\frac{2\pi}{11}\tan\frac{5\pi}{11}}≈1.69191}$
Dichoral angles11/2p–11/2–11/2p: π/11 ≈ 16.36364°
11/5p–11/5–11/5p: 7π/11 ≈ 114.54545°
11/2p–4–11/5p: 90°
Central density10
Related polytopes
DualSmall hendecagrammic-grand hendecagrammic duotegum
ConjugatesHendecagonal-small hendecagrammic duoprism, Hendecagonal-hendecagrammic duoprism, Hendecagonal-great hendecagrammic duoprism, Hendecagonal-grand hendecagrammic duoprism, Small hendecagrammic-hendecagrammic duoprism, Small hendecagrammic-great hendecagrammic duoprism, Hendecagrammic-great hendecagrammic duoprism, Hendecagrammic-grand hendecagrammic duoprism, Great hendecagrammic-grand hendecagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame

The small hendecagrammic-grand hendecagrammic duoprism, also known as the 11/2-11/5 duoprism, is a uniform duoprism that consists of 11 small hendecagrammic prisms and 11 grand hendecagrammic prisms, with 2 of each meeting at each vertex.

## Coordinates

The vertex coordinates of a small hendecagrammic-grand hendecagrammic duoprism, centered at the origin and with edge length 4sin(2π/11)sin(5π/11), are given by:

• (2sin(5π/11), 0, 2sin(2π/11), 0),
• (2sin(5π/11), 0, sin(4π/11), ±2sin2(2π/11)),
• (2sin(5π/11), 0, 2sin(2π/11)cos(4π/11), ±2sin(2π/11)sin(4π/11)),
• (2sin(5π/11), 0, 2sin(2π/11)cos(6π/11), ±2sin(2π/11)sin(6π/11)),
• (2sin(5π/11), 0, 2sin(2π/11)cos(8π/11), ±2sin(2π/11)sin(8π/11)),
• (2sin(5π/11), 0, 2sin(2π/11)cos(10π/11), ±2sin(2π/11)sin(10π/11)),
• (2sin(5π/11)cos(2π/11), ±2sin(5π/11)sin(2π/11), 2sin(2π/11), 0),
• (2sin(5π/11)cos(2π/11), ±2sin(5π/11)sin(2π/11), sin(4π/11), ±2sin2(2π/11)),
• (2sin(5π/11)cos(2π/11), ±2sin(5π/11)sin(2π/11), 2sin(2π/11)cos(4π/11), ±2sin(2π/11)sin(4π/11)),
• (2sin(5π/11)cos(2π/11), ±2sin(5π/11)sin(2π/11), 2sin(2π/11)cos(6π/11), ±2sin(2π/11)sin(6π/11)),
• (2sin(5π/11)cos(2π/11), ±2sin(5π/11)sin(2π/11), 2sin(2π/11)cos(8π/11), ±2sin(2π/11)sin(8π/11)),
• (2sin(5π/11)cos(2π/11), ±2sin(5π/11)sin(2π/11), 2sin(2π/11)cos(10π/11), ±2sin(2π/11)sin(10π/11)),
• (2sin(5π/11)cos(4π/11), ±2sin(5π/11)sin(4π/11), 2sin(2π/11), 0),
• (2sin(5π/11)cos(4π/11), ±2sin(5π/11)sin(4π/11), sin(4π/11), ±2sin2(2π/11)),
• (2sin(5π/11)cos(4π/11), ±2sin(5π/11)sin(4π/11), 2sin(2π/11)cos(4π/11), ±2sin(2π/11)sin(4π/11)),
• (2sin(5π/11)cos(4π/11), ±2sin(5π/11)sin(4π/11), 2sin(2π/11)cos(6π/11), ±2sin(2π/11)sin(6π/11)),
• (2sin(5π/11)cos(4π/11), ±2sin(5π/11)sin(4π/11), 2sin(2π/11)cos(8π/11), ±2sin(2π/11)sin(8π/11)),
• (2sin(5π/11)cos(4π/11), ±2sin(5π/11)sin(4π/11), 2sin(2π/11)cos(10π/11), ±2sin(2π/11)sin(10π/11)),
• (2sin(5π/11)cos(6π/11), ±2sin(5π/11)sin(6π/11), 2sin(2π/11), 0),
• (2sin(5π/11)cos(6π/11), ±2sin(5π/11)sin(6π/11), sin(4π/11), ±2sin2(2π/11)),
• (2sin(5π/11)cos(6π/11), ±2sin(5π/11)sin(6π/11), 2sin(2π/11)cos(4π/11), ±2sin(2π/11)sin(4π/11)),
• (2sin(5π/11)cos(6π/11), ±2sin(5π/11)sin(6π/11), 2sin(2π/11)cos(6π/11), ±2sin(2π/11)sin(6π/11)),
• (2sin(5π/11)cos(6π/11), ±2sin(5π/11)sin(6π/11), 2sin(2π/11)cos(8π/11), ±2sin(2π/11)sin(8π/11)),
• (2sin(5π/11)cos(6π/11), ±2sin(5π/11)sin(6π/11), 2sin(2π/11)cos(10π/11), ±2sin(2π/11)sin(10π/11)),
• (2sin(5π/11)cos(8π/11), ±2sin(5π/11)sin(8π/11), 2sin(2π/11), 0),
• (2sin(5π/11)cos(8π/11), ±2sin(5π/11)sin(8π/11), sin(4π/11), ±2sin2(2π/11)),
• (2sin(5π/11)cos(8π/11), ±2sin(5π/11)sin(8π/11), 2sin(2π/11)cos(4π/11), ±2sin(2π/11)sin(4π/11)),
• (2sin(5π/11)cos(8π/11), ±2sin(5π/11)sin(8π/11), 2sin(2π/11)cos(6π/11), ±2sin(2π/11)sin(6π/11)),
• (2sin(5π/11)cos(8π/11), ±2sin(5π/11)sin(8π/11), 2sin(2π/11)cos(8π/11), ±2sin(2π/11)sin(8π/11)),
• (2sin(5π/11)cos(8π/11), ±2sin(5π/11)sin(8π/11), 2sin(2π/11)cos(10π/11), ±2sin(2π/11)sin(10π/11)),
• (2sin(5π/11)cos(10π/11), ±2sin(5π/11)sin(10π/11), 2sin(2π/11), 0),
• (2sin(5π/11)cos(10π/11), ±2sin(5π/11)sin(10π/11), sin(4π/11), ±2sin2(2π/11)),
• (2sin(5π/11)cos(10π/11), ±2sin(5π/11)sin(10π/11), 2sin(2π/11)cos(4π/11), ±2sin(2π/11)sin(4π/11)),
• (2sin(5π/11)cos(10π/11), ±2sin(5π/11)sin(10π/11), 2sin(2π/11)cos(6π/11), ±2sin(2π/11)sin(6π/11)),
• (2sin(5π/11)cos(10π/11), ±2sin(5π/11)sin(10π/11), 2sin(2π/11)cos(8π/11), ±2sin(2π/11)sin(8π/11)),
• (2sin(5π/11)cos(10π/11), ±2sin(5π/11)sin(10π/11), 2sin(2π/11)cos(10π/11), ±2sin(2π/11)sin(10π/11)).