<Verb>ZigZagContractedComplex(K):: PureCubicalComplex --> PureCubicalComplex</Verb>
<Verb>ZigZagContractedComplex(K):: FilteredPureCubicalComplex --> FilteredPureCubicalComplex</Verb>
<Verb>ZigZagContractedComplex(K):: PurePermComplex --> PurePermComplex</Verb>

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




