Combinatorial geometry is concerned with combinatorial properties and constructive methods of discrete geometric objects. Questions on this topic are on packing, covering, coloring, folding, symmetry, tiling, partitioning, decomposition, and illumination problems.
Combinatorial geometry (a term coined by H. Hadwiger in 1955) comprises the study of geometric objects arranged and combined with regard to discrete properties, esp. incidence relations. It is in this sense a strict subset of discrete and computational geometry topics.
Some representative results in this area are Helly's theorem and Pick's theorem. Recent formal verification of Hales' proposed proof of Kepler's conjecture demonstrates the breadth of tools from analysis as well as discrete mathematics that are useful. Many open problems have been proposed in this area.