# Hendecagrammic-dodecagonal duoprism

Hendecagrammic-dodecagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx11/3o x12o
SymmetryI2(11)×I2(12), order 528
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(3π/11) (base 1), (6+2)/2 (base 2), 2 (sides)
Cells12 hendecagrammic prisms, 11 dodecagonal prisms
Faces132 squares, 12 hendecagrams, 11 dodecagons
Edges132+132
Vertices132
Measures (edge length 1)
Circumradius$\sqrt{2+\sqrt{3}+\frac{1}{4\sin^2\frac{3\pi}{11}}}≈2.04200$ Hypervolume$\frac{33(2+\sqrt{3})}{4\tan\frac{3\pi}{11}}≈26.67918$ Dichoral angles11/3p–11/3–11/3p: 150°
Twip–12–twip: 5π/11 ≈ 81.81818°
11/3p–4–twip: 90°
Central density3
Related polytopes
DualHendecagrammic-dodecagonal duotegum
ConjugatesHendecagonal-dodecagonal duoprism, Hendecagonal-dodecagrammic duoprism, Small hendecagrammic-dodecagonal duoprism, Small hendecagrammic-dodecagrammic duoprism, Hendecagrammic-dodecagrammic duoprism, Great hendecagrammic-dodecagonal duoprism, Great hendecagrammic-dodecagrammic duoprism, Grand hendecagrammic-dodecagonal duoprism, Grand hendecagrammic-dodecagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame

The hendecagrammic-dodecagonal duoprism, also known as the 11/3-12 duoprism, is a uniform duoprism that consists of 12 hendecagrammic prisms and 11 dodecagonal prisms, with 2 of each meeting at each vertex.

The name can also refer to the small hendecagrammic-dodecagonal duoprism, the great hendecagrammic-dodecagonal duoprism, or the grand hendecagrammic-dodecagonal duoprism.

## Vertex coordinates

The coordinates of a hendecagrammic-dodecagonal duoprism, centered at the origin and with edge length 2sin(3π/11), are given by:

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