# Great enneagrammic-decagonal duoprism

(Redirected from 10-9/4 duoprism)
Great enneagrammic-decagonal duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymGistdedip
Info
Coxeter diagramx9/4o x10o
SymmetryI2(9)×I2(10), order 360
ArmySemi-uniform edidip
RegimentGistdedip
Elements
Vertex figureDigonal disphenoid, edge lengths 2cos(4π/9) (base 1), (5+5)/2 (base 2), 2 (sides)
Cells10 great enneagrammic prisms, 9 decagonal prisms
Faces90 squares, 10 great enneagrams, 9 decagons
Edges90+90
Vertices90
Measures (edge length 1)
Circumradius$\sqrt{\frac{1}{4\sin^2\frac{4\pi}{9}}+\frac{3+\sqrt{5}}{2}}≈1.69582$ Hypervolume$\frac{45\sqrt{5+2\sqrt{5}}}{8\tan\frac{4\pi}{9}}≈3.05257$ Dichoral anglesGistep–9/4–gistep: 144°
Dip–10–dip: 20°
Gistep–4–dip: 90°
Central density4
Related polytopes
DualGreat enneagrammic-decagonal duotegum
ConjugatesEnneagonal-decagonal duoprism, Enneagonal-decagrammic duoprism, Enneagrammic-decagonal duoprism, Enneagrammic-decagrammic duoprism, Great enneagrammic-decagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame

The great enneagrammic-decagonal duoprism, also known as gistdedip or the 9/4-10 duoprism, is a uniform duoprism that consists of 10 great enneagrammic prisms and 9 decagonal prisms, with 2 of each meeting at each vertex.

## Vertex coordinates

The coordinates of a great enneagrammic-decagonal duoprism, centered at the origin and with edge length 2sin(4π/9), are given by:

• (1, 0, ±sin(4π/9), ±sin(4π/9)5+25),
• (1, 0, ±sin(4π/9)(3+5)/2, ±sin(4π/9)(5+5)/2),
• (1, 0, ±sin(4π/9)(1+5), 0),
• (cos(2π/9), ±sin(2π/9), ±sin(4π/9), ±sin(4π/9)5+25),
• (cos(2π/9), ±sin(2π/9), ±sin(4π/9)(3+5)/2, ±sin(4π/9)(5+5)/2),
• (cos(2π/9), ±sin(2π/9), ±sin(4π/9)(1+5), 0),
• (cos(4π/9), ±sin(4π/9), ±sin(4π/9), ±sin(4π/9)5+25),
• (cos(4π/9), ±sin(4π/9), ±sin(4π/9)(3+5)/2, ±sin(4π/9)(5+5)/2),
• (cos(4π/9), ±sin(4π/9), ±sin(4π/9)(1+5), 0),
• (–1/2, ±3/2, ±sin(4π/9), ±sin(4π/9)5+25),
• (–1/2, ±3/2, ±sin(4π/9)(3+5)/2, ±sin(4π/9)(5+5)/2),
• (–1/2, ±3/2, ±sin(4π/9)(1+5), 0),
• (cos(8π/9), ±sin(8π/9), ±sin(4π/9), ±sin(4π/9)5+25),
• (cos(8π/9), ±sin(8π/9), ±sin(4π/9)(3+5)/2, ±sin(4π/9)(5+5)/2),
• (cos(8π/9), ±sin(8π/9), ±sin(4π/9)(1+5), 0).