Lars Onsager showed in 1948 that there could be a new type of phase transition where a liquid loses rotational symmetry but retains its translational symmetry, unlike the freezing transition where a liquid loses both types of symmetry operations. He proposed that this is what takes place when a liquid becomes a nematic liquid crystal, a material now extensively used in displays. As more complex forms of liquid-crystallinity were discovered, it became evident in the 1980s, through studies of the Landau theory of phase transitions, that there was a deep connection between liquid crystals, the mathematics of the spherical harmonics Y(M,L), the theory of representations of groups.
More recently, it was proposed by Lorman and Rochal that the shape of viral capsids should be viewed as belonging to the class of orientational phase transitions except for significantly larger values of L than were considered before. In the colloquium I will review the earlier work and then examine the proposal of Lorman and Rochal, applying the Landau theory of orientational transitions of chiral materials.