The paper deals with the optimal control problem that arises when one studies the 4 sphere artificial swimmer at low Reynolds number. Composed of four spheres at the end of extensible arms, the swimmer is known to be able to swim in all directions and orientations in the 3D space. In this paper, optimal strokes, in terms of the energy expended by the swimmer to reach a prescribed net displacement, are fully described in the regime of small strokes. In particular, we introduce a bivector formalism to model the displacements that turns out to be elegant and practical. Numerical simulations are also provided that confirm the theoretical predictions.