ChainComplex(K):: CubicalComplex --> ChainComplex
ChainComplex(K):: PureCubicalComplex --> ChainComplex
ChainComplex(K):: PurePermComplex --> ChainComplex
ChainComplex(Y):: RegCWComplex --> ChainComplex
ChainComplex(K):: SimplicialComplex --> ChainComplex

Inputs a cubical, or pure cubical, or pure permutahedral or simplicial complex K and returns its chain complex of free abelian groups. In degree n this chain complex has one free generator for each n-dimensional cell of K.

Inputs a regular CW-complex Y and returns a chain complex C which is chain homotopy equivalent to the cellular chain complex of Y. In degree n the free abelian chain group C_n has one free generator for each critical n-dimensional cell of Y with respect to some discrete vector field on Y.