To quantitatively estimate lattice free energies, we build and expand on our earlier work , where we identified several useful heuristics for applying reweighed PGMs to obtain accurate free energy estimates. In Ref. , we used isolated small molecules in a vacuum as representative case studies, with 3N -9 out of 3N -6 of the relevant intramolecular degrees of freedom (DOFs) represented using internal coordinates . Those PGMs relied on a mixed coordinate representation of the given molecule. Specifically, we kept three of the atoms represented in Cartesian coordinates to serve as a starting point for a bijective reconstruction of all remaining atoms of the molecule from the internal coordinates. We referred to these three Cartesian atoms as the Cartesian block. When dealing with isolated molecules in a vacuum, the Cartesian block only has three relevant DOFs. However, in systems containing more than one molecule, like crystal supercells, all nine DOFs of the Cartesian block of each molecule must be jointly modelled by the PGM. Here, we use flowbased PGMs to compute the Helmholtz FE differences between crystal supercells using two ice polymorphs (Ic and XI) as simple but representative examples of systems requiring the explicit representation of all nine DOFs for all Cartesian blocks. For such systems, it is important to consider the most cost-effective way of representing a Cartesian block inside the PGM. In this regard, we highlight Ref. , which has contributed a powerful method of representing the Cartesian block based on a unit-quaternion to describe the rotational state of a given molecule.