An Enriques surface X is a smooth compact complex surface having irregularity and nontrivial canonical sheaf such that (Endraß). Such surfaces cannot be embedded in projective three-space, but there nonetheless exist transformations onto singular surfaces in projective three-space. There exists a family of such transformed surfaces of degree six which passes through each edge of a tetrahedron twice. A subfamily with tetrahedral symmetry is given by the two-parameter (r, c) family of surfaces

and the polynomial is a sphere with radius r,


(Endraß).