In general, one aspect of the subject matter described in this specification features a torquer apparatus that includes a rotor with magnetic poles such that, when radially projected on a concentric octahedron, the same symmetrical pattern is obtained on all faces of the octahedron, the polarity of the poles projected on two adjacent faces of the octahedron being opposite. A stator with at least twenty poles magnetized with coils and such that, when radially projected on a concentric icosahedron, the same symmetrical pattern is obtained on all faces of the icosahedron, the stator being-in nominal position-concentric with the rotor. Real-time measurements, or equivalent information, of the position of the rotor with respect to the stator, and real-time measurements, or equivalent information, of exported torque from the stator, or of the orientation of the rotor with respect to the stator can be obtained. A controller for controlling the current in the coils based on the measurements, or the equivalent information, such that the rotor is magnetically held in the nominal position, and that the desired torque is exported.