Generalized cube

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Generalized cube
Rank3
Dimension3
TypeRegular
SpaceComplex
Notation
Coxeter diagram
Schläfli symbolp{4}2{3}2
Elements
Faces3p  γ p
2
 
Edges2p 2  p-edges
Verticesp 3 
Vertex figureTriangle
Related polytopes
Real analogp -gonal trioprism
Abstract & topological properties
Flag count6p 3 
Properties
Symmetryp[4]2[3]2, order 6p 3 

The generalized cubes, γ p
3
 
, are a family of regular complex polyhedra. They generalize the cube, a real polyhedron, to complex space.

The generalized cubes are the rank-3 members of the broader class of generalized hypercubes.

Vertex coordinates[edit | edit source]

Vertex coordinates for the generalized square γ p
3
 
can be given as:

  • ,

where m , n , and o  are integers ranging between 1 and p  inclusive.

Coxeter diagrams[edit | edit source]

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

  • (full symmetry)
  • (p[4]2[2]p symmetry. Prism of a generalized square with a p -edge.)
  • (p[2]p[2]p symmetry. p -edge trioprim.)