The Pm/3n 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 liquidcrystalline phase representing a tetrahedral network of rods with a Pm/3n 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.