We highlight with first-principles molecular dynamics the persistence of intrinsic < 111 > Ti off-centerings for BaTiO3 in its cubic paraelectric phase. Intriguingly, these are inconsistent with the Pm (3) over barm space group often used to atomistically model this phase using density-functional theory or similar methods. Therefore, we deploy a systematic symmetry analysis to construct 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. We define as structural prototypes the smallest of these that are both energetically and dynamically stable. Remarkably, two 40-atom prototypes can be identified for paraelectric BaTiO3; these are also common to many other ABO(3) perovskites. These prototypes can offer structural models of paraelectric phases that can be used for the computational engineering of functional materials. Last, we show that the emergence of B-cation off-centerings and the primitive-cell phonon instabilities is controlled by the equilibrium volume, in turn, dictated by the filler A cation.