ResolutionBieberbachGroup(G):: MatrixGroup --> FreeResolution
ResolutionBieberbachGroup(G,v):: MatrixGroup, List --> FreeResolution

Inputs a torsion free crystallographic group G, also known as a Bieberbach group, represented using AffineCrystGroupOnRight as in the GAP package Cryst. It also optionally inputs a choice of vector v in the Euclidean space \mathbb R^n on which G acts freely. The function returns n+1 terms of the free ZG-resolution of \mathbb Z arising as the cellular chain complex of the tessellation of \mathbb R^n by the Dirichlet-Voronoi fundamental domain determined by v. No contracting homotopy is returned with the resolution.

This function is part of the HAPcryst package written by Marc Roeder and thus requires the HAPcryst package to be loaded.

The function requires the use of Polymake software.