A series of T-shaped polyphilic molecules composed of a rigid linear biphenyl core with a polar glycerol group at each end and one swallow-tail semi-perfluorinated lateral chain were synthesized and their thermotropic liquid crystalline (LC) phases were investigated by X-ray diffraction, calorimetry, and microscopy. The compounds have a long alkyl spacer between the aromatic core and the fluorinated CnF2n+1 ends, where n = 4, 6, 8, and 10. Upon melting, all compounds start with lamellar LC phases, followed on heating by a rectangular columnar ribbon phase with c2mm symmetry. Unusually, a ribbon is a flat bundle of molecular cores highly aligned parallel to the ribbon axis. On further heating, for n = 8 and 10, this phase is succeeded by a bicontinuous cubic phase with Ia (3) over bard symmetry. This is a new variant of the "gyroid" phase, with axially oriented rod-like molecular cores forming the skeleton of the two infinite networks and junctions separated by exactly two molecular lengths. In this tricontinuous core-shell structure (aromatic-aliphatic-perfluoroalkyl), the polar glycerol domains of appreciable size, contained within the skeleton, can be considered as micellar.