  We introduce a new model for a pairwise repulsive interaction potential of
vortices in a type-II superconductor, consisting of superimposed six- and
12-fold anisotropies. Using numerical simulations we study how the vortex
lattice configuration varies as the magnitudes of the two anisotropic
interaction terms change. A triangular lattice appears for all values, and
rotates through 30 degrees as the ratio of the six- and 12-fold anisotropy
amplitudes is varied. The transition causes the VL to split into domains that
have rotated clockwise or counter-clockwise, with domain boundaries that are
"decorated" by dislocations consisting of five- and seven-fold coordinated
vortices. We also find intra-domain dislocations and defects, and characterize
them in terms of their energy cost. We discuss how this model could be
generalized to other particle-based systems with anisotropic interactions, such
as colloids, and consider the limit of very large anisotropy where it is
possible to create cluster crystal states.
