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The scattering pattern of a crystal obeys the symmetry of the crystal structure through the corresponding Laue group. This is usually also true for the diffuse scattering, containing information about disorder, but here a case is reported where the diffuse scattering is of lower symmetry than the parent crystal structure. The mineral bixbyite has been studied by X-ray and neutron scattering techniques since 1928 with some of the most recent studies characterizing the low-temperature transition to a magnetically disordered spin-glass state. However, bixbyite also exhibits structural disorder, and here single-crystal X-ray and neutron scattering is used to characterize the different modes of disorder present. One-dimensional rods of diffuse scattering are observed in the cubic mineral bixbyite, which break the expected symmetry of the scattering pattern. It is shown that this scattering arises from epitaxial intergrowths of the related mineral, braunite. The presence of this disorder mode is found to be directly observable as well-defined residuals in the average structure refined against the Bragg diffraction. An additional three-dimensional diffuse scattering component is observed in neutron scattering data, which is shown to originate from the substitutional disorder on the Fe/Mn sites. This occupational disorder gives rise to local relaxations of the oxide sublattice, and the pattern of oxide displacements can be rationalized based on crystal-field theory. The combined use of neutron and X-ray single-crystal scattering techniques highlights their great complementarity. In particular, the large sample requirements for neutron scattering experiments prove to be an obstacle in solving the intergrowth disorder due to several growth orientations, whereas for X-ray scattering the one-dimensional nature of the intergrowth disorder renders solving this a more tractable task. On the other hand, the oxide relaxations cannot be resolved using X-rays due to the low Mn/Fe contrast. By combining the two approaches both types of disorder have been characterized.