  We continue the project begun in ``The periodic table of $n$-categories for
low dimensions I'' by examining degenerate tricategories and comparing them
with the structures predicted by the Periodic table. For triply degenerate
tricategories we exhibit a triequivalence with the partially discrete
tricategory of commutative monoids. For the doubly degenerate case we explain
how to construct a braided monoidal category from a given doubly degenerate
category, but show that this does not induce a straightforward comparison
between \bfseries{BrMonCat} and \bfseries{Tricat}. We show how to alter the
natural structure of \bfseries{Tricat} in two different ways to provide a
comparison, but show that only the more brutal alteration yields an
equivalence. Finally we study degenerate tricategories in order to give the
first fully algebraic definition of monoidal bicategories and the full
tricategory structure \bfseries{MonBicat}.
