On singularities of the inverse problems associated with perfect cuboids
  Two cubic equations and three auxiliary equations for edges and face diagonals of a rational perfect cuboid have been recently derived. They constitute a background for two inverse problems. The coefficients of cubic equations and the right hand sides of auxiliary equations are rational functions of two rational parameters, i. e. they have denominators. Hence the inverse problems have singular points. These singular points are studied in the present paper. 
John Ramsden, Ruslan Sharipov
math.NT