Finite or discrete collections of geometric objects. Packings, tilings, polyhedra, polytopes, intersection, arrangements, rigidity.

Discrete Geometry includes the study of combinatorial and other aspects of finite or discrete collections of geometric object. It is closely related to combinatorial topology, convex geometry, combinatorial geometry, computational geometry, geometric graph theory and the study of polyhedra and polytopes.

Typical objects of study include circle-, sphere- and other packings, tessellations, arrangements of hyperplanes, configuration spaces, matroids, and lattices.

Methods used to study these objects reach from algebraic geometry, algebraic topology, number theory and graph theory to discrete mathematics, combinatorics and optimization.

history | excerpt history