  By the Three Graces we refer, following J.-L. Loday, to the algebraic operads
Ass, Com, and Lie, each generated by a single binary operation; algebras over
these operads are respectively associative, commutative associative, and Lie.
We classify all distributive laws (in the categorical sense of Beck) between
these three operads. Some of our results depend on the computer algebra system
Maple, especially its packages LinearAlgebra and Groebner.
