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What is the face lattice of a convex polytope

The *face poset* of a convex polyhedron is
the set of all faces of ordered by set inclusion.
Two polytopes are called *isomorphic* if
their face posets are isomorphic.
The face poset of a convex polytope is a lattice.

The face poset of a convex polyhedron is sometimes
referred to as the *combinatorial structure* of the polyhedron.
Thus the expression ``two polyhedra are combinatorially equal''
means they are isomorphic.

Komei Fukuda
2004-08-26