The package ”VertexEnumeration” contains Mathematica implementations of Avis-Fukuda algorithms for enumerating all vertices of a convex polytope given by a system of linear inequalities, and for enumerating all points (0-dimensional faces) of an arrangement of hyperplanes given similarly. The package also generates Voronoi diagrams and graphs. The supplementary package ”FaceLattice.m” computes the face lattice structure of a bounded convex polyhedron.