# Pentagonal-hendecagonal duoprism

(Redirected from 11-5 duoprism)
Pentagonal-hendecagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymPahendip
Info
Coxeter diagramx5o x11o
SymmetryH2×I2(11), order 220
ArmyPahendip
RegimentPahendip
Elements
Vertex figureDigonal disphenoid, edge lengths (1+5)/2 (base 1), 2cos(π/11) (base 2), and 2 (sides)
Cells11 pentagonal prisms, 5 hendecagonal prisms
Faces55 squares, 11 pentagons, 5 hendecagons
Edges55+55
Vertices55
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{5+\sqrt5}{10}+\frac{1}{4\sin^2\frac{\pi}{11}}} ≈ 1.96807}$
Hypervolume${\displaystyle \frac{11\sqrt{25+10\sqrt5}}{16\tan\frac{\pi}{11}}≈16.11337}$
Dichoral anglesPip–5–pip: ${\displaystyle \frac{9\pi}{11} ≈ 147.27273°}$
Henp–11–henp: 108°
Pip–4–henp: 90°
Central density1
Euler characteristic0
Number of pieces16
Level of complexity6
Related polytopes
DualPentagonal-hendecagonal duotegum
ConjugatesPentagonal-small hendecagrammic duoprism, Pentagonal-hendecagrammic duoprism, Pentagonal-great hendecagrammic duoprism, Pentagonal-grand hendecagrammic duoprism, Pentagrammic-hendecagonal duoprism, Pentagrammic-small hendecagrammic duoprism, Pentagrammic-hendecagrammic duoprism, Pentagrammic-great hendecagrammic duoprism, Pentagrammic-grand hendecagrammic duoprism
Properties
ConvexYes
OrientableYes
NatureTame

The pentagonal-hendecagonal duoprism or pahendip, also known as the 5-11 duoprism, is a uniform duoprism that consists of 5 hendecagonal prisms and 11 pentagonal prisms, with two of each joining at each vertex.

## Vertex coordinates

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

• (±sin(π/11), –sin(π/11)(5+25)/5, 1, 0),
• (±sin(π/11), –sin(π/11)(5+25)/5, cos(2π/11), ±sin(2π/11)),
• (±sin(π/11), –sin(π/11)(5+25)/5, cos(4π/11), ±sin(4π/11)),
• (±sin(π/11), –sin(π/11)(5+25)/5, cos(6π/11), ±sin(6π/11)),
• (±sin(π/11), –sin(π/11)(5+25)/5, cos(8π/11), ±sin(8π/11)),
• (±sin(π/11), –sin(π/11)(5+25)/5, cos(10π/11), ±sin(10π/11)),
• (±sin(π/11)(1+5)/2, sin(π/11)(5–5)/10, 1, 0),
• (±sin(π/11)(1+5)/2, sin(π/11)(5–5)/10, cos(2π/11), ±sin(2π/11)),
• (±sin(π/11)(1+5)/2, sin(π/11)(5–5)/10, cos(4π/11), ±sin(4π/11)),
• (±sin(π/11)(1+5)/2, sin(π/11)(5–5)/10, cos(6π/11), ±sin(6π/11)),
• (±sin(π/11)(1+5)/2, sin(π/11)(5–5)/10, cos(8π/11), ±sin(8π/11)),
• (±sin(π/11)(1+5)/2, sin(π/11)(5–5)/10, cos(10π/11), ±sin(10π/11)),
• (0, 2sin(π/11)(5+5)/10, 1, 0),
• (0, 2sin(π/11)(5+5)/10, cos(2π/11), ±sin(2π/11)),
• (0, 2sin(π/11)(5+5)/10, cos(4π/11), ±sin(4π/11)),
• (0, 2sin(π/11)(5+5)/10, cos(6π/11), ±sin(6π/11)),
• (0, 2sin(π/11)(5+5)/10, cos(8π/11), ±sin(8π/11)),
• (0, 2sin(π/11)(5+5)/10, cos(10π/11), ±sin(10π/11)).