The Al₂SiO₅ polymorphs (andalusite, kyanite, and sillimanite), which are widespread in aluminous metamorphic rocks, are gaining importance as industrial sources for producing aluminum oxide, silumin, and aluminum. On the other hand, the “triple point”, which corresponds to the equilibrium coexistence of all three Al2SiO5 polymorphs, is one of the key invariant points in metamorphic petrology. Mineral assemblages with triple-point polymorphs provide reference information for the calibration of geothermobarometers and for identification of isotope indicator features and some other geochemical parameters. The polymetamorphic history of a series of metamorphic complexes of Al-rich metapelites in the Yenisei Range, with rocks containing an Al silicate triple-point assemblage (all three Al₂SiO₅ polymorphs), is illustrated by structural-geological, mineralogical–petrological, and isotope geochronological evidence. In the studied aureoles, overprinting of later mineral assemblages onto earlier ones during various geodynamic events obviously follows from the reaction microtextures and chemical zoning in minerals, the РT trajectories of these rocks, as well as radiometric dating. These indicator features show that the Al₂SiO₅ polymorphs grew sequentially as a result of a complex polymetamorphic history due to changes in the tectonic environments. A comparative analysis of the new results and the literature on other metamorphic regions worldwide shows that the Al₂SiO₅ minerals always (at least in the studied rocks) occur in reaction relationships with one another, grew at different time periods during the metamorphic history of the rocks, and hence, cannot be regarded as true triple point assemblages, although some segments of the looping PT paths may pass near the triple point. We conclude that the aluminum silicate triple-point assemblages, in which all three Al₂SiO₅ minerals are in stable equilibrium, are not possible in metapelitic rocks of any chemical composition. Hence, such purported triple-point assemblages cannot represent a stable association and cannot be used to calibrate or test geothermobarometers.