An Enriques surface
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 () family of surfaces
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 (
) family of surfaces
is a sphere with radius 
,
