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A stable decagonal phase of a new structural type was discovered in Al—Pd—Re. This is the second Al-based alloy system after Al—Pd—Mn where both stable icosahedral and decagonal phases are formed. In contrast to the isostructural icosahedral phases of similar Al and Pd concentrations in both systems, the new decagonal phase exhibits periodicity of ∼2.57 vs. ∼1.25 nm in Al—Pd—Mn and is formed at significantly higher Al concentration than that in Al—Pd—Mn. In the tenfold plane, the structural unit of the Al—Pd—Re decagonal phase assumed from the high-resolution electron images is