A sequence of liquid crystalline phases, involving cybotactic nematics, a lamellar phase, bicontinuous cubics and triangular honeycombs, was observed for oligo(phenylene ethynylene) based X-shaped bolapolyphiles with two long lateral alkyl chains and sticky ends provided by glycerol groups. In the cubic phase with Ia3[combining macron]d lattice - which is tailored by alkyl chain engineering - the aromatic cores are organized on the gyroid minimal surface in 3D curved layers of almost parallel aligned π-conjugated rods. It is shown that this type of cubic phase is a general mode of soft self-assembly of X-shaped bolapolyphiles at the cross-over from the (long or short range) lamellar to the triangular honeycomb-like organization. Cubic phase formation is found only in a narrow range with respect to temperature and chain-length for the non-fluorinated compounds and in much wider ranges for related core-fluorinated molecules.