The Pm n cubic and other low-symmetry Frank-Kasper phases are known to be formed by soft spheres, ranging from metals to block copolymer micelles and colloidal nanoparticles. Here, we report a series of X-shaped polyphiles composed of sticky rods and two non-symmetric branched side-chains, which self-assemble into the first example of a cubic liquid-crystalline phase representing a tetrahedral network of rods with a Pm n lattice. It is the topological dual to the Weaire-Phelan foam, being the Voronoi tessellation of the A15 sphere packing, from which this network is obtained by Delaunay triangulation.
Keywords: Cubic Liquid Crystals; Delaunay Triangulation; Frank-Kasper Phases; Self-Assembly; Tetrahedral Networks.
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