Résumé:

In the present work we give a clear-cut explanation of the unusual pentagonal protein arrangement in viral capsids from the viewpoint of solid state physics, namely theory of quasicrystals (QC). We show that the systems considered represent the first example of matter organization in 2D nanoparticles, in which the regions with a chiral pentagonal quasicrystallineorder of protein positions are arranged in a structure commensurate with the spherical topology and dodecahedral geometry. We establish the relations between the elastic properties of these unconventional QC regions and the unusual structure and geometry of the resulting viral capsid.