In this account recent progress in enhancing the complexity of liquid crystal self-assembly is highlighted. The discussed superstructures are formed mainly by polyphilic T-shaped and X-shaped molecules composed of a rod-like core, tethered with glycerol units at both ends and flexible non-polar chain(s) in lateral position, but also related inverted molecular structures are considered. A series of honeycomb phases composed of polygonal cylinders ranging from triangular to hexagonal, followed by giant cylinder honeycombs is observed for ternary T-shaped polyphiles on increasing the size of the lateral chain(s). Increasing the chain size further leads to new modes of lamellar organization followed by three-dimensional and two-dimensional structures incorporating branched and non-branched axial rod-bundles. Grafting incompatible chains to opposite sides of the rod-like core leads to quaternary X-shaped polyphiles. These form liquid crystalline honeycombs where different cells are filled with different material. Projected on an Euclidian plane, all honeycomb phases can be described either by uniformly coloured Archimedean and Laves tiling patterns (T-shaped polyphiles) or as multi-colour tiling patterns (X-shaped polyphiles). It is shown that geometric frustration, combined with the tendency to segregate incompatible chains into different compartments and the need to find a periodic tiling pattern, leads to a significant increase in the complexity of soft self-assembly. Mixing of different chains greatly enhances the number of possible ‘colours’ and in this way, periodic structures comprising up to seven distinct compartments can be generated. Relations to biological self-assembly are discussed shortly.