On the example of exceptional families of viruses we i) show the existence of
a completely new type of matter organization in nanoparticles, in which the
regions with a chiral pentagonal quasicrystalline order of protein positions
are arranged in a structure commensurate with the spherical topology and
dodecahedral geometry, ii) generalize the classical theory of quasicrystals
(QCs) to explain this organization, and iii) establish the relation between
local chiral QC order and nonzero curvature of the dodecahedral capsid faces.Comment: 8 pages, 3 figure