Smectic phases with cubic symmetry: The splay analog of the blue phase

We report on a construction for smectic blue phases, which have quasi-long-range smectic translational order as well as long-range cubic or hexagonal order. Our proposed structures fill space with a combination of minimal surface patches and cylindrical tubes. We find that for the right range of material parameters, the favorable saddle-splay energy of these structures can stabilize them against uniform layered structures.