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On the example of exceptional families of viruses we i) show the existence ofa completely new type of matter organization in nanoparticles, in which theregions with a chiral pentagonal quasicrystalline order of protein positionsare arranged in a structure commensurate with the spherical topology anddodecahedral geometry, ii) generalize the classical theory of quasicrystals(QCs) to explain this organization, and iii) establish the relation betweenlocal chiral QC order and nonzero curvature of the dodecahedral capsid faces.

Chiral Quasicrystalline Order and Dodecahedral Geometry in Exceptional Families of Viruses