ZigZagContractedComplex(K):: PureCubicalComplex --> PureCubicalComplex
ZigZagContractedComplex(K):: FilteredPureCubicalComplex --> FilteredPureCubicalComplex
ZigZagContractedComplex(K):: PurePermComplex --> PurePermComplex

Inputs a pure cubical, filtered pure cubical or pure permutahedral complex and returns a homotopy equivalent complex. In the filtered case, the t-th term of the output is homotopy equivalent to the t-th term of the input for all t.