The Lopéz-Ros deformation tilts the ends of the doubly periodic Scherk surface:

This has the undesirable side effect that the surfaces are no longer embedded. However, the added flexibility might be useful for gluing constructions. For instance, it might be possible to desingularize the intersections by singly periodic Scherk surfaces. The result could look on either side like one half of a triply periodic minimal surface, but the entire surface would be embedded and only doubly periodic.

Resources

Mathematica Notebook

PoVRay Sources