In some common posets such as the face lattice of a convex polytope there is a natural grading by dimension, which if used as rank function would give the minimal element, the empty face, rank −1. In such cases it might be convenient to bend the definition stated above by adjoining the value −1 to the set of values allowed for the rank function. Allowing arbitrary integers as rank would however give a fundamentally different notion; for instance the existence of a minimal element would no longer be assured.
