  The topologies permitted in joint ocular dominance (OD), orientation
preference (OP), and direction preference (DP) maps in the primary visual
cortex (V1) are considered, with the aim of finding a maximally symmetric
periodic case that can serve as the basis for perturbations toward natural
realizations. It is shown that mutual consistency of the maps selects just two
possible such lattice structures, and that one of these is much closer to
experiment than the other. This comprises a hexagonal lattice of alternating
positive and negative OP singularities, with each unit cell or hypercolumn
containing four such singularities, each radiating three DP discontinuities
that follow OP contours and end at OP singularities of opposite sign. Other DP
discontinuities emanate at 90 degrees to the midpoints of the ones that link OP
singularities, and cross OP contours perpendicularly. These features explain
experimentally observed relationships between DP discontinuities and OP
contours, including sudden approximately 90-degree changes of direction in the
former.

Biological Physics