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 R² and R³ 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 Rⁿ whose nonempty intersections are contractible. We also give sufficient (and trivially necessary) conditions on a locally finite collection of contractible polyhedra in R² or R³ for their nonempty intersections to be contractible.