  Given two convex polytopes, the join, the cartesian product and the direct
sum of them are well understood. In this paper we extend these three kinds of
products to abstract polytopes and introduce a new product, called the
topological product, which also arises in a natural way.
  We show that these products have unique prime factorization theorems.
  We use this to compute the automorphism group of a product in terms of the
automorphism groups of the factors and show that (non trivial) products are
almost never regular or two-orbit polytopes. We finish the paper by studying
the monodromy group of a product, show that such a group is always an extension
of a symmetric group, and give some examples in which this extension splits.
