Element lattice

Every polytope is made out of elements which are contained in others. By considering all elements under the membership relation, one obtains the element lattice of the polytope, more commonly known as the face lattice in mathematical literature.

If one considers element lattices on their own and specifies the properties that make them valid, one obtains the concept of abstract polytopes.

The term originated from convex polytopes, whose element lattices are always mathematical lattices. Perhaps misleadingly, the element lattice of a general polytope is not always a lattice.