# Pentagonal-grand hendecagrammic duoprism

(Redirected from 11/5-5 duoprism)
Pentagonal-grand hendecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx5o x11/5o
SymmetryH2×I2(11), order 220
ArmySemi-uniform pahendip
Elements
Vertex figureDigonal disphenoid, edge lengths (1+5)/2 (base 1), 2cos(5π/11) (base 2), 2 (sides)
Cells11 pentagonal prisms, 5 grand hendecagrammic prisms
Faces55 squares, 11 pentagons, 5 grand hendecagrams
Edges55+55
Vertices55
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{5+\sqrt{5}}{10}+\frac{1}{4\sin^2\frac{5\pi}{11}}}≈0.98933}$
Hypervolume${\displaystyle \frac{11\sqrt{5(5+2\sqrt{5})}}{16\tan\frac{5\pi}{11}}≈0.68026}$
Dichoral anglesPip–5–pip: π/11 ≈ 16.36364°
11/5p–11/5–11/5p: 108°
Pip–4–11/5p: 90°
Central density5
Related polytopes
DualPentagonal-grand hendecagrammic duotegum
ConjugatesPentagonal-hendecagonal duoprism, Pentagonal-small hendecagrammic duoprism, Pentagonal-hendecagrammic duoprism, Pentagonal-great hendecagrammic duoprism, Pentagrammic-hendecagonal duoprism, Pentagrammic-small hendecagrammic duoprism, Pentagrammic-hendecagrammic duoprism, Pentagrammic-great hendecagrammic duoprism, Pentagrammic-grand hendecagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame

The pentagonal-grand hendecagrammic duoprism, also known as the 5-11/5 duoprism, is a uniform duoprism that consists of 11 pentagonal prisms and 5 grand hendecagrammic prisms, with two of each meeting at each vertex.

## Vertex coordinates

The coordinates of a pentagonal-grand hendecagrammic duoprism, centered at the origin and with edge length 2sin(5π/11), are given by:

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