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A perfect cuboid is a rectangular parallelepiped whose edges, whose facediagonals, and whose space diagonal are of integer lengths. The problem offinding such cuboids or proving their non-existence is not solved thus far. Thesecond cuboid conjecture specifies a subclass of perfect cuboids described byone Diophantine equation of tenth degree and claims their non-existence withinthis subclass. Regardless of proving or disproving this conjecture in thepresent paper the Diophantine equation associated with it is studied and isused in order to build an optimized strategy of computer-assisted search forperfect cuboids within the subclass covered by the second cuboid conjecture.

A strategy of numeric search for perfect cuboids in the case of the second cuboid conjecture