Once a suitable ideal triangulation is found, SnapPea can try to find a hyperbolic structure. In his Princeton lecture notes, Thurston noted a method for describing the geometric shape of each hyperbolic tetrahedron by a complex number and a set of nonlinear equations of complex variables whose solution would give a complete hyperbolic metric on the 3-manifold. These equations consist of "edge equations" and "cusp (completeness) equations". SnapPea uses an iterative method utilizing Newton's method to search for solutions. If no solution exists, then this is reported to the user.