  A pentagonal order formed by 360 proteins in the bovine papilloma viral
capsid and structures of some smaller viral capsids are considered from a
unified point of view based on the Landau crystallization theory. To simulate
the capsid structures we map the planar pentagonal Penrose quasilattice (PPQ)
constructed in the frames of the Landau theory onto a sphere through the
dodecahedron nets of different sizes. Six different simplest nets containing
from 60 to 360 positions occupied by proteins are proposed. Buckling of the
initially planar capsid faces and a smooth conjugation of the protein orders at
the adjacent faces are taken into account by means of two conditions imposed on
the minimization of the capsid free energy. This conditional minimization
results in two-component phason strain field, which describes the
self-consistent reconstruction of quasicrystalline orders located at twelve
faces of spherical dodecahedron. All six chiral structures obtained in this way
are very similar to those of well-known spherical viral capsids. The theory
proposed explains some general peculiarities of protein organization in capsids
of small and medium-sized viruses.
