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The crystalline structure of nuclear matter is investigated in the standardSkyrme model with massive pions. A semi-analytic method is developed todetermine local minima of the static energy functional with respect tovariations of both the field and the period lattice of the crystal. Fourdistinct Skyrme crystals are found. Two of these were already known -- thecubic lattice of half-skyrmions and the $\alpha$-particle crystal -- but twoare new. These new solutions have lower energy per baryon number and lesssymmetry, being periodic with respect to trigonal but not cubic periodlattices. Minimal energy crystals are also constructed under the constraint ofconstant baryon density, and its shown that the two new non-cubic crystals tendto chain and multi-wall solutions at low densities.

Skyrme crystals with massive pions