Low-temperature vesuvianites crystallize in the two space groups P4/n or P4nc due to different arrangements of Ca-dodecahedra and M2+,3+ square pyramids that form strings along the fourfold axes. Long-range ordered vesuvianites of acentric P4nc symmetry may have the same diffraction symmetry as centrosymmetric disordered P4/nnc vesuvianites. In contrast, P4/n long-range ordered vesuvianites exhibit glide plane violating reflections and can easily be identified. We report the first successful X-ray single-crystal structure refinement of a P4nc vesuvianite, a = 15.487(2), c = 11.764(2) Å from the N’chwaning II mine of the Kalahari manganese fields (RSA). This untwinned crystal has Cu2+ and Mn2+, Mn3+ forming the square pyramid and exhibits an acentric ordering pattern with 85% string A and 15% string B. This is compared to a reinvestigation of the structure of a P4/n vesuvianite from Asbestos Quebec (Canada), a = 15.531(2), c = 11.817(2) Å. The crystal is composed of a merohedral (110) twin with a close to 1:1 twin ratio and has mainly Fe3+ in square pyramidal coordination. In this centric structure, string A is 84% and string B is 16% occupied. Criteria to determine the symmetry of low-temperature vesuvianites, studied by diffraction experiments, are discussed.