  Polytope numbers for a polytope are a sequence of nonnegative integers that
are defined by the facial information of a polytope. Every polygon is
triangulable and a higher dimensional analogue of this fact states that every
polytope is triangulable, namely, every polytope can be decomposed into
simplexes. Thus it may be possible to represent polytope numbers by sums of
simplex numbers. We analyzes a special type of triangulation, called pointed
triangulation, and develops several methods to represent polytope numbers by
sums of simplex numbers.
