Finite noncrystallographic groups, 11-vertex equi-edged triangulated clusters and polymorphic transformations in metals

The one-to-one correspondence between a set of cosets of the Mathieu group M₁₁, block sets of the Steiner system S(4, 5, 11) and 11-vertex equi-edged triangulated clusters determines symmetry-allowable transformations between different 11-vertex triangulated clusters as automorphisms of the Steiner system S(4, 5, 11). The transformations can describe local reconstructions corresponding to polymorphic transformations in metals.