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When one uses ISIF=3 we allow the unit cell shape, volume and the ions to relax.

How is the unit cell shape relaxed; what algorithm does the code use in relaxing those? (like it uses forces for ionic relaxation) Once you allow cell shape relaxation how does one impose any particular crystal structure on the calculation? The lattice parameters, then, are essentially free to vary totally independently, right?

The crystal structure I have is a P-421c point group #114 which has two variable lattice parameters a and b. And also 3 internal degrees of freedom x,y and z for the atom basis. So if I startout with the experimental values in my POSCAR and relax it using ISIF=3 is the structure guranteed to remain in the tetragonal group?

Appreciate any guidance on this!

Yes, if you choose isif=3 every lattice parameter is free to relax.
Read also http://cms.mpi.univie.ac.at/vasp/vasp/node103.html.
Vasp analysis the symmetry at the beginning of the calculation, so you this will not change during the relaxation, unless you change to isym=0 (no symmetry at all).

the cell shapes/ volumes are relaxed according to the stress tensors.
concerning the change of structure using ISIF=3:
if ISYM is not switched off explicitely (ISYM=0 of -1), the symmetry
of the lattice is determined (from the Bravais matrix, the ions' positions, the velocities and the magnetic moments) at the beginning of a vasp run. All forces are symmetrized with respect to the symmetry operations of that lattice type. Hence, during a cell shape/V relaxation, the symmetry of the input lattice is perserved (though e.g. c/a may change for a hcp lattice).