# Pentagrammic-great enneagrammic duoprism

(Redirected from 5/2-9/4 duoprism)
Pentagrammic-great enneagrammic duoprism
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymStagstedip
Info
Coxeter diagramx5/2o x9/4o
SymmetryH2×I2(9), order 180
ArmySemi-uniform peendip
RegimentStagstedip
Elements
Vertex figureDigonal disphenoid, edge lengths (5–1)/2 (base 1), 2cos(4π/9) (base 2), 2 (sides)
Cells9 pentagrammic prisms, 5 great enneagrammic prisms
Faces45 squares, 9 pentagrams, 5 great enneagrams
Edges45+45
Vertices45
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{5-\sqrt{5}}{10}+\frac{1}{4\sin^2\frac{4\pi}{9}}}≈0.73087}$
Hypervolume${\displaystyle \frac{9\sqrt{5(5-2\sqrt{5})}}{16\tan\frac{4\pi}{9}}≈0.16113}$
Dichoral anglesStip–5/2–stip: 20°
Gistep–9/4–gistep: 36°
Stip–4–gistep: 90°
Central density8
Related polytopes
DualPentagrammic-great enneagrammic duotegum
ConjugatesPentagonal-enneagonal duoprism, Pentagonal-enneagrammic duoprism, Pentagonal-great enneagrammic duoprism, Pentagrammic-enneagonal duoprism, Pentagrammic-enneagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame

The pentagrammic-great enneagrammic duoprism, also known as stagstedip or the 5/2-9/4 duoprism, is a uniform duoprism that consists of 9 pentagrammic prisms and 5 great enneagrammic prisms, with 2 of each meeting at each vertex.

## Vertex coordinates

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

• (±sin(4π/9), –sin(4π/9)(5–25)/5, 1, 0),
• (±sin(4π/9), –sin(4π/9)(5–25)/5, cos(2π/9), ±sin(2π/9)),
• (±sin(4π/9), –sin(4π/9)(5–25)/5, cos(4π/9), ±sin(4π/9)),
• (±sin(4π/9), –sin(4π/9)(5–25)/5, –1/2, ±3/2),
• (±sin(4π/9), –sin(4π/9)(5–25)/5, cos(8π/9), ±sin(8π/9)),
• (±sin(4π/9)(5–1)/2, sin(4π/9)(5+5)/10, 1, 0),
• (±sin(4π/9)(5–1)/2, sin(4π/9)(5+5)/10, cos(2π/9), ±sin(2π/9)),
• (±sin(4π/9)(5–1)/2, sin(4π/9)(5+5)/10, cos(4π/9), ±sin(4π/9)),
• (±sin(4π/9)(5–1)/2, sin(4π/9)(5+5)/10, –1/2, ±3/2),
• (±sin(4π/9)(5–1)/2, sin(4π/9)(5+5)/10, cos(8π/9), ±sin(8π/9)),
• (0, –2sin(4π/9)(5–5)/10, 1, 0),
• (0, –2sin(4π/9)(5–5)/10, cos(2π/9), ±sin(2π/9)),
• (0, –2sin(4π/9)(5–5)/10, cos(4π/9), ±sin(4π/9)),
• (0, –2sin(4π/9)(5–5)/10, –1/2, ±3/2),
• (0, –2sin(4π/9)(5–5)/10, cos(8π/9), ±sin(8π/9)).