Novel bolapolyphiles, built of a p-terphenyl or bistolane core with polar glycerol end-groups and two laterally attached n-alkyl or semiperfluoroalkyl chains, form the first "single plumber's nightmare network", the simplest soft-matter cubic phase (Pm3̅m). Its cage-like grid comprises bundles of aromatic rods lying along the cubic unit cell edges, connected by six-way hydrogen-bonded junctions. Side-chains fill the remaining volume of this unique noninterpenetrating liquid-crystalline organic framework.