The three-particle operator in a second quantized form is studied. The
operator is transformed into irreducible tensor form. Possible coupling
schemes, distinguished by the classes of symmetric group \mathrm{S_{6}}, are
presented. Recoupling coefficients, which allow one to transform given scheme
into another, are produced by using the angular momentum theory, combined with
quasispin formalism. The classification of three-particle operator, which acts
on n=1,2,...,6 open shells of equivalent electrons of atom, is considered. The
procedure to construct three-particle matrix elements are examined
