# Decagrammic-grand hendecagrammic duoprism

(Redirected from 11/5-10/3 duoprism)
Decagrammic-grand hendecagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Info
Coxeter diagramx10/3o x11/5o
SymmetryI2(10)×I2(11), order 440
ArmySemi-uniform dahendip
Elements
Vertex figureDigonal disphenoid, edge lengths (5–5)/2 (base 1), 2cos(5π/11) (base 2), 2 (sides)
Cells11 decagrammic prisms, 10 grand hendecagrammic prisms
Faces11 decagrams, 10 grand hendecagrams, 110 squares
Edges110+110
Vertices110
Measures (edge length 1)
Circumradius$\sqrt{\frac{3-\sqrt{5}}{2}+\frac{1}{4\sin^2\frac{5\pi}{11}}}≈0.79821$ Hypervolume$\frac{55\sqrt{5-2\sqrt{5}}}{8\tan\frac{5\pi}{11}}≈0.71817$ Dichoral anglesStiddip–10/3–stiddip: π/11 ≈ 16.36364°
11/5p–11/5–11/5p: 72°
Stiddip–4–11/5p: 90°
Central density15
Related polytopes
DualDecagrammic-grand hendecagrammic duotegum
ConjugatesDecagonal-hendecagonal duoprism, Decagonal-small hendecagrammic duoprism, Decagonal-hendecagrammic duoprism, Decagonal-great hendecagrammic duoprism, Decagonal-grand hendecagrammic duoprism, Decagrammic-hendecagonal duoprism, Decagrammic-small hendecagrammic duoprism, Decagrammic-hendecagrammic duoprism, Decagrammic-great hendecagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame

The decagrammic-grand hendecagrammic duoprism, also known as the 10/3-11/5 duoprism, is a uniform duoprism that consists of 11 decagrammic prisms and 10 grand hendecagrammic prisms, with 2 of each meeting at each vertex.

## Coordinates

The vertex coordinates of a decagrammic-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, 1, 0),
• (±sin(5π/11), ±sin(5π/11)5–25, cos(2π/11), ±sin(2π/11)),
• (±sin(5π/11), ±sin(5π/11)5–25, cos(4π/11), ±sin(4π/11)),
• (±sin(5π/11), ±sin(5π/11)5–25, cos(6π/11), ±sin(6π/11)),
• (±sin(5π/11), ±sin(5π/11)5–25, cos(8π/11), ±sin(8π/11)),
• (±sin(5π/11), ±sin(5π/11)5–25, cos(10π/11), ±sin(10π/11)),
• (±sin(5π/11)(3–5)/2, ±sin(5π/11)(5–5)/2, 1, 0),
• (±sin(5π/11)(3–5)/2, ±sin(5π/11)(5–5)/2, cos(2π/11), ±sin(2π/11)),
• (±sin(5π/11)(3–5)/2, ±sin(5π/11)(5–5)/2, cos(4π/11), ±sin(4π/11)),
• (±sin(5π/11)(3–5)/2, ±sin(5π/11)(5–5)/2, cos(6π/11), ±sin(6π/11)),
• (±sin(5π/11)(3–5)/2, ±sin(5π/11)(5–5)/2, cos(8π/11), ±sin(8π/11)),
• (±sin(5π/11)(3–5)/2, ±sin(5π/11)(5–5)/2, cos(10π/11), ±sin(10π/11)),
• (±sin(5π/11)(5–1), 0, 1, 0),
• (±sin(5π/11)(5–1), 0, cos(2π/11), ±sin(2π/11)),
• (±sin(5π/11)(5–1), 0, cos(4π/11), ±sin(4π/11)),
• (±sin(5π/11)(5–1), 0, cos(6π/11), ±sin(6π/11)),
• (±sin(5π/11)(5–1), 0, cos(8π/11), ±sin(8π/11)),
• (±sin(5π/11)(5–1), 0, cos(10π/11), ±sin(10π/11)).