Abstract

An enantiomorphous 240-vertex “diamond structure” is considered in the space of a three-dimensional sphere S3, whose highly symmetric clusters determined by the subconfigurations of finite projective planes PG(2, q), q = 2, 3, 4 are the specific clusters of diamond-like structures. The classification of the generating clusters forming diamond-like structures is introduced. It is shown that the symmetry of the configuration, in which the configuration setting the generating clusters is embedded, determines the symmetry of diamond-like structures. The sequence of diamond-like structures (from a diamond to a BC8 structure) is also considered. On an example of the construction of PG(2, 3), it is shown with the aid of the summation and multiplication tables of the Galois field GF(3) that the generalized crystallography of diamond-like structures provides more possibilities than classical crystallography because of the transition from groups to algebraic constructions in which at least two operations are defined.

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