CubicalComplexFactory

alg_top.spad line 3651 [edit on github]

Provides functions to construct various Cubical complexes. For more information see: http://www.euclideanspace.com/prog/scratchpad/mycode/topology/cubical/factory/

band: () -> FiniteCubicalComplex Integer

Generate a cubical complex of the surface of a cylinder without ends

kleinBottle: () -> FiniteCubicalComplex Integer

generate a cubical complex of the surface of a Klein bottle.

moebiusBand: () -> FiniteCubicalComplex Integer

Generate a cubical complex of the surface of a Moebius band. A one sided surface with a single external boundary line.

projectiveSpace: NonNegativeInteger -> FiniteCubicalComplex Integer

Generate a cubical complex of the surface of a projective plane. A one sided surface which cannot be embedded in 3D space without intersecting itself. There are no external boundaries, every edge connects two faces. (A punctured projective plane is equivalent to a Moebius band)

sphereSolid: NonNegativeInteger -> FiniteCubicalComplex Integer

Generate a cubical complex equivalent to a solid hyper-sphere. That is, a solid volume with no holes in it, so we use a single n-dimensional cube.

sphereSurface: NonNegativeInteger -> FiniteCubicalComplex Integer

Generate a cubical complex equivalent to the surface of a hyper-sphere. That is, the surface of a volume with no holes in it, so we use the faces of a single cube.

torusSurface: () -> FiniteCubicalComplex Integer

generate a cubical complex of the surface of an 3-dimensional torus.