Nerve(M):: PureCubicalComplex --> SimplicialComplex
Nerve(M):: PurePermComplex --> SimplicialComplex
Nerve(M,n):: PureCubicalComplex, Int --> SimplicialComplex
Nerve(M,n):: PurePermComplex, Int --> SimplicialComplex

Inputs a pure cubical complex or pure permutahedral complex M and returns the simplicial complex K obtained by taking the nerve of an open cover of |M|, the open sets in the cover being sufficiently small neighbourhoods of the top-dimensional cells of |M|. The spaces |M| and |K| are homotopy equivalent by the Nerve Theorem. If an integer n \ge 0 is supplied as the second argument then only the n-skeleton of K is returned.