Bicontinuous cubic liquid crystalline phases of π-conjugated molecules, representing self-assembled 3D-ordered interpenetrating networks with cubic symmetry, are receiving increasing attention due to their capacity for charge transport in all three dimensions and their inherent spontaneous helicity. Herein, a robust general design concept for creating bicontinuous cubic phases is reported. It is based on a nonsymmetric-substituted π-conjugated 5,5′-diphenyl-2,2′-bithiophene platform with one end containing three outfanning flexible chains and with a range of substituents at the other end (the apex). The cubic phases are stable over broad temperature ranges, often down to ambient temperature, and tolerate a wide range of apex substitution patterns, allowing structural diversity and tailoring of the cubic phase type and application-relevant properties. With an increasing number and size of apex substituents, a sequence of three different modes of cubic self-assembly is observed, following an increasing helical twist. Thus, two ranges of the achiral double network Ia3d phase range can be distinguished, a long pitch and a short pitch, with the chiral triple network I23 cubic phase in the intermediate pitch range. The findings provide a new prospect for the directed design of cubic phase-forming functional materials based on spontaneously formed helical network liquid crystals with tunable application specific properties.