Strongly normal sets of contractible tiles in N dimensions

The second and third authors and others have studied collections of (usually) convex “tiles”—a generalization of pixels or voxels—in R2R2 and R3R3 that have a property called strong normality (SN): for any tile P, only finitely many tiles intersect P, and any nonempty intersection of those tiles also intersects P  . This paper extends basic results about strong normality to collections of contractible polyhedra in RnRn whose nonempty intersections are contractible. We also give sufficient (and trivially necessary) conditions on a locally finite collection of contractible polyhedra in R2R2 or R3R3 for their nonempty intersections to be contractible.