Abstract. The piezoelectric switching of antiferroelectric domains by the simultaneous application of an electric field Ei and mechanical stress Tk is proposed as a direct method for examining whether some spinel compositions do have point symmetry 33m and concomitant antiferroelectric ordering as proposed by Grimes.For piezoelectric antiferroelectrics, the switching energy is Ag = 2dij,Ei7;, (d,,, = piezoelectric coefficient). For point symmetry 43m, various possible switching procedures have been described in detail. The smallest coercive product of electric field and stress (E,T,k), is required for switching when the electric field is chosen along cubic [OOl], and directional stress along [llO] or [lTO]. For particular directions, for example [lll], the colinear application of electric field and stress also leads to switching.If the assumed prototype with space group F33m -t h e symmetry proposed by Grimesis supposed to undergo a phase transition leading to ferrimagnetism, the possible symmetries ofthe ferrimagnetic domains are given by the magnetic groups 14m'2', Im'm2 and R3m'. which are M-maximal subgroups of the prototype magnetic group Fz3ml'. All three ferrimagnetic phases permit piezoelectricity, piezomagnetism and the linear and second-order magnetoelectric effect. The tetragonal phase (15m'27 remains antiferroelectric as the prototype is supposed to be, whereas the orthorhombic (Im'm27 and trigonal (R3m') phases become ferroelectric. The full lattice of subgroups of FiT3ml' is presented.