Structural properties of encapsidated flexible polyelectrolytes in viral capsids with dodecahedral charge distribution have been investigated by Monte Carlo simulations using a coarse-grained model. Several capsid charge distributions ranging from a homogeneous surface charge distribution (lambda=0) to a complete dodecahedral distribution (lambda=1) at constant total capsid charge and fixed radial location of the capsid charges have been considered. The radial and lateral organizations of the polyelectrolyte have been examined as a function of the polyelectrolyte length and capsid charge distribution. With short polyelectrolytes a single polyelectrolyte layer was formed at the inner capsid surface, whereas at increasing polyelectrolyte length also a uniform polyelectrolyte density inside the surface layer was established. At low lambda , the polyelectrolyte layer was laterally isotropic, but at lambda> or =0.05 a dodecahedral structure started to appear. At lambda=1 , the polyelectrolyte followed essentially a path along the edges of a dodecahedron. With sufficiently long chains, all edges were decorated with polyelectrolyte, facilitated by loop formation. For an undercharged capsid, the capsid counterions inside the capsid also adopted a dodecahedral distribution.