Pattern quarks and leptons

Disclinations, concave and convex, are the canonical point defects of two-dimensional planar patterns in systems with translational and rotational symmetries. From these, all other point defects (vortices, dislocations, targets, saddles and handles) can be built. Moreover, handles, coupled concave-convex disclination pairs arise as instabilities, symmetry breaking events. The purpose of this article is to show that embedded in three or more dimensions, concave and convex disclination strings, two-dimensional disclinations with loop backbones, have interesting and suggestive invariant indices which are integer multiples of.