  A rational perfect cuboid is a rectangular parallelepiped whose edges and
face diagonals are given by rational numbers and whose space diagonal is equal
to unity. It is described by a system of four quadratic equations with respect
to six variables. The cuboid factor equations were derived from these four
equations by symmetrization procedure. They constitute a system of eight
polynomial equations. Recently two sets of formulas were derived providing two
solutions for the cuboid factor equations. These two solutions are studied in
the present paper. They are proved to coincide with each other up to a change
of parameters in them.
