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In this Letter we report brand new analytic stationary solutions of constant density stars with magnetic field and self-gravity. These solutions include prolate configurations even for purely poloidal magnetic fields as well as oblate configurations. These new analytic solutions are expressed in very simple forms and can be considered as generalized configurations of uniformly rotating constant density spheroids, i.e. Maclaurin spheroids, and of constant density ellipsoids with constant vorticity, i.e. Dedekind ellipsoids. As the axisymmetric Maclaurin spheroids and the triaxial Dedekind ellipsoids have been widely used for the estimation of the effect of rotations and/or internal motions on the self-gravitating bodies, our new analytic solutions may be used widely to estimate the effect of the magnetic fields semi-quantitatively in various contexts hereafter.