# Square-great enneagrammic duoprism

Square-great enneagrammic duoprism
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)
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

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)).