<p>Geologists have been debating for decades whether or not the Al₂SiO₅ polymorphs (andalusite, kyanite and sillimanite) can coexist with one another in thermodynamic equilibrium in natural rocks at the P–T conditions of the triple point. Such rocks have not yet been reliably identified in nature. The technique of thermodynamic-potential minimization allows us to determine the bulk rock, fluid composition and other factors that could influence the stability of Al₂SiO₅ polymorphs. In this theoretical study, the stable equilibrium coexistence of all three polymorphs was considered in mineral assemblages comprising plagioclase ± quartz ± paragonite ± graphite, biotite ± muscovite ± quartz ± magnetite ± graphite and at the P–T conditions of the triple point. It is shown how the hydrogen, oxygen and carbon-content in a metamorphic fluid can influence both the stable mineral assemblage and the equilibrium coexistence of the Al₂SiO₅ polymorphs. The effect of such elements as Na, Fe, Mg, Mn, Ti and P was studied using the bulk composition of a natural rock sample. A series of restrictions on the bulk composition of the mineral assemblage comprising Al₂SiO₅ polymorphs have been identified.</p>