This work details how to determine structural prototypes for the cubic perovskite structure that are used to study the B-site displacements in the cubic, paraelectric phase. Car-Parrinello MD simulations of cubic barium titanate (BaTiO3) show the titanium displacements from the undistorted cubic structure. Using a systematic symmetry analysis we construct microscopic templates, i.e. representative structural models in the form of supercells that satisfy a desired point symmetry but are built from the combination of lower-symmetry primitive cells. Density functional theory calculations, using the microscopic templates as starting structures for a relaxation, are carried out to find structural prototypes of BaTiO3 with local polar distortions but with cubic point symmetry. The stability of these structures is studied as a function of volume and with respect to the zone-boundary phonons of pristine cubic BaTiO3. The stable distortions patterns for BaTiO3 are investigated for other titanates and for a handful of niobates and zirconates.