  Geometric lattices are characterized in this paper as those finite, atomic
lattices such that every atom ordering induces a lexicographic shelling given
by an edge labeling known as a minimal labeling. Equivalently, geometric
lattices are shown to be exactly those finite lattices such that every ordering
on the join-irreducibles induces a lexicographic shelling. This new
characterization fits into a similar paradigm as McNamara's characterization of
supersolvable lattices as those lattices admitting a different type of
lexicographic shelling, namely one in which each maximal chain is labeled with
a permutation of {1,...,n}.
