# Hendecagrammic-dodecagrammic duoprism

Hendecagrammic-dodecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx11/3o x12/5o
SymmetryI2(11)×I2(12), order 528
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(3π/11) (base 1), (62)/2 (base 2), 2 (sides)
Cells12 hendecagrammic prisms, 11 dodecagrammic prisms
Faces12 hendecagrams, 11 dodecagrams, 132 squares
Edges132+132
Vertices132
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{1}{4\sin^2\frac{3\pi}{11}}+2-\sqrt{3}}≈0.84003}$
Hypervolume${\displaystyle \frac{33(2-\sqrt{3})}{4\tan\frac{3\pi}{11}}≈1.91548}$
Dichoral angles11/3p–11/3–11/3p: 30°
12/5p–12/5–12/5p: 5π/11 ≈ 81.81818°
11/3p–4–12/5p: 90°
Central density15
Related polytopes
DualHendecagrammic-dodecagrammic duotegum
ConjugatesHendecagonal-dodecagonal duoprism, Hendecagonal-dodecagrammic duoprism, Small hendecagrammic-dodecagonal duoprism, Small hendecagrammic-dodecagrammic duoprism, Hendecagrammic-dodecagonal duoprism, Great hendecagrammic-dodecagonal duoprism, Great hendecagrammic-dodecagrammic duoprism, Grand hendecagrammic-dodecagonal duoprism, Grand hendecagrammic-dodecagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame

The hendecagrammic-dodecagrammic duoprism, also known as the 11/3-12/5 duoprism, is a uniform duoprism that consists of 12 hendecagrammic prisms and 11 dodecagrammic prisms, with 2 of each meeting at each vertex.

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

## Coordinates

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

• (1, 0, ±sin(3π/11)(3–1), ±sin(3π/11)(3–1)),
• (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)(3–1), ±sin(3π/11)(3–1)),
• (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)(3–1), ±sin(3π/11)(3–1)),
• (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)(3–1), ±sin(3π/11)(3–1)),
• (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)(3–1), ±sin(3π/11)(3–1)),
• (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)(3–1), ±sin(3π/11)(3–1)),
• (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)).