A note on solutions of the cuboid factor equations

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.