γ  3,3

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γ 3
3
 
Rank3
Dimension3
TypeRegular
SpaceComplex
Notation
Coxeter diagram
Schläfli symbol3{4}2{3}2
Elements
Faces9 γ 3
2
 
Edges18 3-edges
Vertices27
Vertex figureTriangle
Related polytopes
Real analogTriangular trioprism
Dualβ 3
3
 
Abstract & topological properties
Flag count162
Properties
Symmetry3[4]2[3]2, order 162

γ 3
3
 
is a regular complex polyhedron. It is the simplest generalized cube other than the real cube.

Vertex coordinates[edit | edit source]

Vertex coordinates for the generalized square γ 3
3
 
can be given as all permutations of:

  • ,
  • ,
  • ,
  • .

Coxeter diagrams[edit | edit source]

A generalized cube γ 3
3
 
can be represented by the following Coxeter diagrams:

  • (full symmetry)
  • (3[4]2[2]3 symmetry. Prism of γ 3
    2
     
    with a 3-edge.)
  • (3[2]3[2]3 symmetry. 3-edge trioprim.)