Binary high temperature “Al3Mn” (T-phase) and its extensions in ternary systems were the subjects of numerous crystallographic investigations. The results were ambiguous regarding the existence or lack of the center of symmetry: both Pna21 and Pnam space groups were reported. Our research on the Al–Mn–Pt T-phase allowed concluding that inside a continuous homogeneity region, the structure of the Al-rich T-phase (e.g., Al78Mn17.5Pt4.5) belongs to the non-centrosymmetric Pna21 space group, while the structure of the Al-poor T-phase (such as Al71.3Mn25.1Pt3.6) is centrosymmetric, i.e., Pnam. Following metallurgical and crystallographic considerations, the change in the symmetry was explained.