# Hendecagonal-dodecagonal duoprism

Hendecagonal-dodecagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx11o x12o
SymmetryI2(11)×I2(12), order 528
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(π/11) (base 1), (2+6)/2 (base 2), and 2 (sides)
Cells12 hendecagonal prisms, 11 dodecagonal prisms
Faces132 squares, 12 hendecagons, 11 dodecagons
Edges132+132
Vertices132
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{2+\sqrt3+\frac{1}{4\sin^2\frac{\pi}{11}}} ≈ 2.62330}$
Hypervolume${\displaystyle \frac{33(2+\sqrt3)}{4\tan\frac{\pi}{11}} ≈ 104.85913}$
Dichoral anglesHenp–11–henp: 150°
Twip–12–twip: ${\displaystyle \frac{9\pi}{11} ≈ 147.27273°}$
Henp–4–twip: 90°
Central density1
Euler characteristic0
Number of pieces23
Level of complexity6
Related polytopes
DualHendecagonal-dodecagonal duotegum
ConjugatesHendecagonal-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-dodecagonal duoprism, Grand hendecagrammic-dodecagrammic duoprism
Properties
ConvexYes
OrientableYes
NatureTame

The hendecagonal-dodecagonal duoprism or hentwadip, also known as the 11-12 duoprism, is a uniform duoprism that consists of 11 dodecagonal prisms and 12 hendecagonal prisms, with two of each joining at each vertex.

## Vertex coordinates

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

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

## Representations

A hendecagonal-dodecagonal duoprism has the following Coxeter diagrams:

• x11o x12o (full symmetry)
• x6x x11o (dodecagons as dihexagons)