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. (C) 2010 Elsevier Inc All rights reserved