# Pentagrammic-great hendecagrammic duoprism

(Redirected from 5/2-11/4 duoprism)
Pentagrammic-great hendecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx5/2o x11/4o
SymmetryH2×I2(11), order 220
ArmySemi-uniform pahendip
Elements
Vertex figureDigonal disphenoid, edge lengths (5–1)/2 (base 1), 2cos(4π/11) (base 2), 2 (sides)
Cells11 pentagrammic prisms, 5 great hendecagrammic prisms
Faces55 squares, 11 pentagrams, 5 great hendecagrams
Edges55+55
Vertices55
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{5-\sqrt{5}}{10}+\frac{1}{4\sin^2\frac{4\pi}{11}}}≈0.76061}$
Hypervolume${\displaystyle \frac{11\sqrt{5(5-2\sqrt{5})}}{16\tan\frac{4\pi}{11}}≈0.51008}$
Dichoral anglesStip–5/2–stip: 3π/11 ≈ 49.09091°
11/4p–11/4–11/4p: 36°
Stip–4–11/4p: 90°
Central density8
Related polytopes
DualPentagrammic-great hendecagrammic duotegum
ConjugatesPentagonal-hendecagonal duoprism, Pentagonal-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-grand hendecagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame

The pentagrammic-great hendecagrammic duoprism, also known as the 5/2-11/4 duoprism, is a uniform duoprism that consists of 11 pentagrammic prisms and 5 great hendecagrammic prisms, with 2 of each meeting at each vertex.

## Vertex coordinates

The coordinates of a pentagrammic-great hendecagrammic duoprism, centered at the origin and with edge length 2sin(4π/11), are given by:

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