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We report on a construction for smectic blue phases, which have quasi-longrange smectic translational order as well as three dimensional crystallineorder. Our proposed structures fill space by adding layers on top of a minimalsurface, introducing either curvature or edge defects as necessary. We findthat for the right range of material parameters, the favorable saddle-splayenergy of these structures can stabilize them against uniform layeredstructures. We also consider the nature of curvature frustration between meancurvature and saddle-splay.Comment: 15 pages, 11 figure

Smectic blue phases: Layered systems with high intrinsic curvature