# Grand hendecagrammic-dodecagonal duoprism

Grand hendecagrammic-dodecagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx11/5o x12o
SymmetryI2(11)×I2(12), order 528
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(5π/11) (base 1), (6+2)/2 (base 2), 2 (sides)
Cells12 grand hendecagrammic prisms, 11 dodecagonal prisms
Faces132 squares, 12 grand hendecagrams, 11 dodecagons
Edges132+132
Vertices132
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{2+\sqrt{3}+\frac{1}{4\sin^2\frac{5\pi}{11}}}≈1.99680}$
Hypervolume${\displaystyle \frac{33(2+\sqrt{3})}{4\tan\frac{5\pi}{11}}≈4.42685}$
Dichoral angles11/5p–11/5–11/5p: 150°
Twip–12–twip: π/11 ≈ 16.36364°
11/5p–4–twip: 90°
Central density5
Related polytopes
DualGrand hendecagrammic-dodecagonal duotegum
ConjugatesHendecagonal-dodecagonal duoprism, Hendecagonal-dodecagrammic duoprism, Small hendecagrammic-dodecagonal duoprism, Small hendecagrammic-dodecagrammic duoprism, Hendecagrammic-dodecagonal duoprism, Hendecagrammic-dodecagrammic duoprism, Great hendecagrammic-dodecagonal duoprism, Great hendecagrammic-dodecagrammic duoprism, Grand hendecagrammic-dodecagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame

The grand hendecagrammic-dodecagonal duoprism, also known as the 11/5-12 duoprism, is a uniform duoprism that consists of 12 grand hendecagrammic prisms and 11 dodecagonal prisms, with 2 of each meeting at each vertex.

## Vertex coordinates

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

• (1, 0, ±sin(5π/11)(1+3), ±sin(5π/11)(1+3)),
• (1, 0, ±sin(5π/11), ±sin(5π/11)(2+3)),
• (1, 0, ±sin(5π/11)(2+3), ±sin(5π/11)),
• (cos(2π/11), ±sin(2π/11), ±sin(5π/11)(1+3), ±sin(5π/11)(1+3)),
• (cos(2π/11), ±sin(2π/11), ±sin(5π/11), ±sin(5π/11)(2+3)),
• (cos(2π/11), ±sin(2π/11), ±sin(5π/11)(2+3), ±sin(5π/11)),
• (cos(4π/11), ±sin(4π/11), ±sin(5π/11)(1+3), ±sin(5π/11)(1+3)),
• (cos(4π/11), ±sin(4π/11), ±sin(5π/11), ±sin(5π/11)(2+3)),
• (cos(4π/11), ±sin(4π/11), ±sin(5π/11)(2+3), ±sin(5π/11)),
• (cos(6π/11), ±sin(6π/11), ±sin(5π/11)(1+3), ±sin(5π/11)(1+3)),
• (cos(6π/11), ±sin(6π/11), ±sin(5π/11), ±sin(5π/11)(2+3)),
• (cos(6π/11), ±sin(6π/11), ±sin(5π/11)(2+3), ±sin(5π/11)),
• (cos(8π/11), ±sin(8π/11), ±sin(5π/11)(1+3), ±sin(5π/11)(1+3)),
• (cos(8π/11), ±sin(8π/11), ±sin(5π/11), ±sin(5π/11)(2+3)),
• (cos(8π/11), ±sin(8π/11), ±sin(5π/11)(2+3), ±sin(5π/11)),
• (cos(10π/11), ±sin(10π/11), ±sin(5π/11)(1+3), ±sin(5π/11)(1+3)),
• (cos(10π/11), ±sin(10π/11), ±sin(5π/11), ±sin(5π/11)(2+3)),
• (cos(10π/11), ±sin(10π/11), ±sin(5π/11)(2+3), ±sin(5π/11)).