Liquid crystalline networks composed of pentagonal, square, and triangular cylinders

T-shaped molecules are designed in such a way that they self-organize into nanoscale liquid crystalline honeycombs based on polygons with any chosen number of sides. One of the phases reported here is a periodic organization of identical pentagonal cylinders; the other one is a structure composed of square-shaped and triangular cylinders in the ratio 2:1. These two different packing motifs represent duals of the same topological class. The generalization of the concept applied here allows the prediction of a whole range of unusual complex liquid crystalline phases.