Commuting diagrams in a bicategory

I'm writing up the definitions of braided, sylleptic, and symmetric monoidal bicategories and would like to reorient some of the polyhedral coherence diagrams to make their symmetry more apparent. All the 2-morphisms are isomorphisms and all the 1-morphisms are equivalences. In such a case, it seems like any way of chopping up the polyhedron into two "sides" will commute as long as one way does. Is this common wisdom, or a folk theorem, or has someone proved it? -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com [For admin and other information see: http://www.mta.ca/~cat-dist/ ]