The one-to-one correspondence has been revealed between a set of cosets of the Mathieu group M 11 , a set of blocks of the Steiner system S(4, 5, 11) and 11vertex equi-edged triangulated clusters. The revealed correspondence provides the structure interpretation of the S(4, 5, 11) system: mapping of the biplane 2-(11, 5, 2) onto the Steiner system S(4, 5, 11) determines uniquely the 11-vertex tetrahedral cluster, and the automorphisms of the S(4, 5, 11) system determine uniquely transformations of the said 11-vertex tetrahedral cluster. The said transformations correspond to local reconstructions during polymorphic transformations in metals. The proposed symmetry description of polymorphic transformation in metals is consistent with experimental data.Automorphism of the S(4, 5, 11) Blocks corresponding to 'bottom' tetrahedra of cluster in Fig. 3 No mapping 39 562 34 987 35 40X 4 08 562 60 987 86 40X 4 À1 60 987 86 40X 08 562 2 4 À2 86 40X 08 562 60 987