  In the paper we present a proof of the local criterion for crystalline
structures which generalizes the local criterion for regular systems. A Delone
set is called a crystal if it is invariant with respect to a crystallgraphic
group. So-called locally antipodal Delone sets, i.e. such sets in which all
2R-clusters are centrally symmetrical, are considered. It turns out that the
local antipodal sets have crystalline structure. Moreover, if in a locally
antipodal set all 2R-clusters are the same the set is a regular system, i.e. a
Delone set whose symmetry group operates transitively on the set.
