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A-T-Al aluminides, where A = actinide, lanthanide or rare earth elements and T=transition metals, have attracted considerable attention as potential materials where heavy fermions may be formed. This led to the discovery of superconducting properties in cubic AT₂Al₂₀ compounds with CeCr₂Al₂₀-type crystal structure. Other Al-rich aluminides, belonging to these A-T-Al systems, exhibited different physical properties as a function of their crystal structure. Thus, predicting the stable structure of the Al-richest phase that will form in the A-T-Al systems is highly valuable. Stability of the crystal structures, forming in the CeT₂Al₂₀ and YRe₂Al₂₀ systems, was studied in current research using density functional theory (DFT) calculations. It is demonstrated that the total spin magnetic moment of the transition metal can be used as a descriptor for phase stability assessment in the AT₂Al₂₀ systems, where T is a 5<i>d</i> transition metal. Basing on crystallographic considerations, degree of distortion of the coordination polyhedrons, formed around T atoms, can be directly connected to the specific type of structure crystallizing in these systems.