Dielectric particles suspended in a weakly conducting fluid are known to spontaneously start rotating under the action of a sufficiently strong uniform dc electric field due to the Quincke rotation instability. This rotation can be converted into translation when the particles are placed near a surface providing useful model systems for active matter. Using a combination of numerical simulations and theoretical modeling, we demonstrate that it is possible to convert this spontaneous Quincke rotation into spontaneous translation in a plane perpendicular to the electric field in the absence of surfaces by relying on geometrical asymmetry instead.