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Finite noncrystallographic groups, 11‐vertex equi‐edged triangulated clusters and polymorphic transformations in metals
Author(s) -
Talis Alexander,
Kraposhin Valentin
Publication year - 2014
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s2053273314015733
Subject(s) - vertex (graph theory) , tetrahedron , combinatorics , automorphism , cluster (spacecraft) , transformation (genetics) , mathematics , physics , crystallography , geometry , chemistry , computer science , graph , biochemistry , gene , programming language
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 11‐vertex 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.