  We show that the family of chain modules over the standard simplices can be
equipped with an operad structure. Similarly, the family of cochain modules of
the Stasheff polytopes can be equipped with an operad structure. We first show
that these operads are Koszul dual to each other, and second that they are both
Koszul operads.
  The algebras over the standard simplices operad, called associative
trialgebras, are defined by 3 operations and 11 relations. The algebras over
the Stasheff polytopes operad, called dendriform trialgebras, are defined by 3
operations and 7 relations.
