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A rational perfect cuboid is a rectangular parallelepiped whose edges andface diagonals are given by rational numbers and whose space diagonal is equalto unity. It is described by a system of four equations with respect to sixvariables. The cuboid factor equations were derived from these four equationsby symmetrization procedure. They constitute a system of eight polynomialequations, which has been solved parametrically. In the present paper itsparametric solution is expressed through intersections or rational and ellipticcurves arranged into parametric families.

A note on rational and elliptic curves associated with the cuboid factor equations