  We give an elementary and direct combinatorial definition of opetopes in
terms of trees, well-suited for graphical manipulation and explicit
computation. To relate our definition to the classical definition, we recast
the Baez-Dolan slice construction for operads in terms of polynomial monads:
our opetopes appear naturally as types for polynomial monads obtained by
iterating the Baez-Dolan construction, starting with the trivial monad. We show
that our notion of opetope agrees with Leinster's. Next we observe a suspension
operation for opetopes, and define a notion of stable opetopes. Stable opetopes
form a least fixpoint for the Baez-Dolan construction. A final section is
devoted to example computations, and indicates also how the calculus of
opetopes is well-suited for machine implementation.
