  We develop a method for subdividing polyhedral complexes in a way that
restricts the possible recession cones and allows one to work with a fixed
class of polyhedron. We use these results to construct locally finite
completions of rational polyhedral complexes whose recession cones lie in a
fixed fan, locally finite polytopal completions of polytopal complexes, and
locally finite zonotopal completions of zonotopal complexes.

Combinatorics