A diblock copolymer dissolved in a mixture of partially miscible solvents creates a self-organized microemulsion with a morphology that depends on the numerous parameters of the system. We discuss one particular case of spherical particles (containing the minority solvent) forming a hard gel with cubic structure and demonstrate using high-resolution synchrotron scattering experiments that the self-organized solution has a BCC structure. After fitting one- and two-dimensional form factors we extract from the data the one- and two-dimensional structure factors, S(q) and S(q,phi). The experimental S(q) corresponds almost quantitatively, up to the 9th order Bragg peak, to that calculated numerically for a randomly-oriented, finite-size BCC crystal. S(q,phi) contains a large number of reflections that allow the structure to be identified more exactly as a twin BCC morphology with some imperfections. Examination of the dependence of the structural parameters on polymer concentration reveals that the dilution law predicted theoretically for the center-to-center distance of the spheres is confirmed experimentally while the size of the spherical objects does not follow theoretical predictions due to chain extension with increasing concentration.