Square-great enneagrammic duoprism

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Square-great enneagrammic duoprism
4-9-4 duoprism.png
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymSagstedip
Info
Coxeter diagramx4o x9/4o
SymmetryBC2×I2(9), order 144
ArmySemi-uniform sendip
RegimentSagstedip
Elements
Vertex figureDigonal disphenoid, edge lengths, 2cos(4π/9) (base 1) and 2 (base 2 and sides)
Cells9 cubes, 4 great enneagrammic prisms
Faces9+36 squares, 4 great enneagrams
Edges36+36
Vertices36
Measures (edge length 1)
Circumradius2+csc2(4π/9))/2 ≈ 0.87050
Hypervolume9/[4tan(4π/9)] ≈ 0.39674
Dichoral anglesCube–4–cube: 20°
 Gistep–9/4–gistep: 90°
 Cube–4–gistep: 90°
Central density4
Related polytopes
DualSquare-great enneagrammic duotegum
ConjugatesSquare-enneagonal duoprism, Square-enneagrammic duoprism
Properties
ConvexNo
OrientableYes
NatureTame


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

Vertex coordinates[edit | edit source]

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

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

External links[edit | edit source]