# Cubical Complexes Factory

As an alternative to simplicial complexes we can base our topology on squares rather than triangles.

### Examples of Complexes

 Solid Sphere - In this case 2 dimentional square: ```(1) -> sp := sphereSolid(2)\$CubicalComplexFactory (1) (1..2,1..2) Type: FiniteCubicalComplex(Integer) ``` Sphere Surface - In this case 2 dimentional square sides: ```(2) -> sps := sphereSurface(2)\$CubicalComplexFactory (2) -(1..1,1..2) (2..2,1..2) (1..2,1..1) -(1..2,2..2) Type: FiniteCubicalComplex(Integer)``` Band - Cylinder without ends: ```(3) -> bnd := band()\$CubicalComplexFactory (3) (1..1,1..2,1..2) (2..2,1..2,1..2) (1..2,1..1,1..2) (1..2,2..2,1..2) Type: FiniteCubicalComplex(Integer)``` Torus - ```(4) ->tor := torusSurface()\$CubicalComplexFactory (4) (1..1,1..2,1..1,1..2) (1..1,1..2,2..2,1..2) (1..1,1..2,1..2,1..1) (1..1,1..2,1..2,2..2) (2..2,1..2,1..1,1..2) (2..2,1..2,2..2,1..2) (2..2,1..2,1..2,1..1) (2..2,1..2,1..2,2..2) (1..2,1..1,1..1,1..2) (1..2,1..1,2..2,1..2) (1..2,1..1,1..2,1..1) (1..2,1..1,1..2,2..2) (1..2,2..2,1..1,1..2) (1..2,2..2,2..2,1..2) (1..2,2..2,1..2,1..1) (1..2,2..2,1..2,2..2) Type: FiniteCubicalComplex(Integer)``` Möbius band: One boundary: `not yet implemented` Projective Plane - No boundaries, every edge is connected to two faces: ```(6) -> pp := projectiveSpace(2)\$CubicalComplexFactory (5) (1..2,1..1,1..1,1..2,1..1) (1..2,1..1,1..1,1..1,1..2) (1..1,1..2,1..2,1..1,1..1) (1..1,1..2,1..1,1..2,1..1) (1..1,1..1,1..2,1..1,1..2) (1..2,1..2,2..2,1..1,1..1) (1..2,2..2,1..2,1..1,1..1) (2..2,1..2,1..2,1..1,1..1) (1..2,1..2,1..1,1..1,2..2) (1..2,2..2,1..1,1..1,1..2) (2..2,1..2,1..1,1..1,1..2) (1..2,1..1,1..2,2..2,1..1) (1..2,1..1,2..2,1..2,1..1) (2..2,1..1,1..2,1..2,1..1) (1..1,1..2,1..1,1..2,2..2) (1..1,1..2,1..1,2..2,1..2) (1..1,2..2,1..1,1..2,1..2) (1..1,1..1,1..2,1..2,2..2) (1..1,1..1,1..2,2..2,1..2) (1..1,1..1,2..2,1..2,1..2) Type: FiniteCubicalComplex(Integer)```

### Further Information

For corresponding factory for simpectial complexes see page here.

For more general information about cubical complexes see page here .

My code for this page is on github here.

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see also:
• I have put the code here.
Correspondence about this page

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 Computational Homology - Tomasz Kaczynski, Konstantin Mischaikow, Marian Mrozek - Cubical homology and its potential applications .

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