Editing Discrete geometry (section)

===Packings, coverings and tilings===
{{main|circle packing|tessellation}}

Packings, coverings, and tilings are all ways of arranging uniform objects (typically circles, spheres, or tiles) in a regular way on a surface or [[manifold]].

A '''sphere packing''' is an arrangement of non-overlapping [[sphere]]s within a containing space. The spheres considered are usually all of identical size, and the space is usually three-[[dimension]]al [[Euclidean space]]. However, sphere [[packing problem]]s can be generalised to consider unequal spheres, ''n''-dimensional Euclidean space (where the problem becomes [[circle packing]] in two dimensions, or [[hypersphere]] packing in higher dimensions) or to [[Non-Euclidean geometry|non-Euclidean]] spaces such as [[hyperbolic space]].

A '''tessellation''' of a flat surface is the tiling of a [[plane (mathematics)|plane]] using one or more geometric shapes, called tiles, with no overlaps and no gaps. In [[mathematics]], tessellations can be generalized to higher dimensions.

Specific topics in this area include:
*[[Circle packing]]s
*[[Sphere packing]]s
*[[Kepler conjecture]]
*[[Quasicrystal]]s
*[[Aperiodic tiling]]s
*[[Periodic graph (geometry)|Periodic graph]]
*[[Finite subdivision rule]]s