of carbon atoms arranged to form icosahedral cages [@kroto1], and viral capsids, the protein containers which encapsulate the viral genomic material [@casjens]. Quasicrystals are described mathematically via cut-and-project schemes and model sets [@senechal; @grimm; @moody], which correspond to infinite Delone point sets [@grimm]. On the other hand, the arrangement of proteins in a viral capsid or the atoms of fullerenes are modeled via finite point sets (arrays) with icosahedral symmetry. In particular, Caspar-Klug theory and generalisations thereof [@twarock] predict the locations and relative orientations of the capsid proteins via icosahedral surface lattices. Moreover, the three-dimensional organisation of viral capsids can be modeled via finite nested point sets displaying icosahedral symmetry at each radial level [@keef; @jess; @dechant2; @zappa2] or 3D icosahedral tilings [@david]. Such point sets can be characterised via affine extensions of the icosahedral group [@keef; @jess], the Kac-Moody algebra formalism [@dechant2], or in a finite group theoretical framework [@zappa2]. The latter provides a link between the construction of quasicrystals and point arrays, the common thread being the orthogonal projection of points of a higher dimensional lattice into a space invariant under the icosahedral group.

Quasicrystals undergo structural transitions as a consequence of changes of thermodynamical parameters. Experimental observations 