Square-great enneagrammic duoprism

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Square-great enneagrammic duoprism
Rank4
TypeUniform
Notation
Bowers style acronymSagstedip
Coxeter diagramx4o x9/4o ()
Elements
Cells9 cubes, 4 great enneagrammic prisms
Faces9+36 squares, 4 great enneagrams
Edges36+36
Vertices36
Vertex figureDigonal disphenoid, edge lengths, 2cos(4π/9) (base 1) and 2 (base 2 and sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesGistep–9/4–gistep: 90°
 Cube–4–gistep: 90°
 Cube–4–cube: 20°
Height1
Central density4
Number of external pieces22
Level of complexity12
Related polytopes
ArmySemi-uniform sendip
RegimentSagstedip
DualSquare-great enneagrammic duotegum
ConjugatesSquare-enneagonal duoprism, Square-enneagrammic duoprism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryB2×I2(9), order 144
ConvexNo
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 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:

where j = 2, 4, 8.

Representations[edit | edit source]

A square-great enneagrammic duoprism has the following Coxeter diagrams:

  • x4o x9/4o (full symmetry)
  • x x x9/4o () (I2(9)×A1×A1 symmetry, great enneagrammic prismatic prism)

External links[edit | edit source]