# Hendecagonal-dodecagrammic duoprism

Hendecagonal-dodecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx11o x12/5o
SymmetryI2(11)×I2(12), order 528
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(π/11) (base 1), (62)/2 (base 2), 2 (sides)
Cells12 hendecagonal prisms, 11 dodecagrammic prisms
Faces132 squares, 12 hendecagons, 11 dodecagrams
Edges132+132
Vertices132
Measures (edge length 1)
Circumradius$\sqrt{2–\sqrt{3}+\frac{1}{4\sin^2\frac{\pi}{11}}}≈1.84868$ Hypervolume$\frac{33(2-\sqrt{3})}{4\tan\frac{\pi}{11}}≈7.52855$ Dichoral angles11p–11–11p: 30°
12/5p–12/5–12/5p: 9π/11 ≈ 147.27273°
11p–4–12/5p: 90°
Central density5
Related polytopes
DualHendecagonal-dodecagrammic duotegum
ConjugatesHendecagonal-dodecagonal 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-dodecagonal duoprism, Grand hendecagrammic-dodecagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame

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

## Vertex coordinates

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

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