  We investigate ternary products of groupoids and prove that there is a
one-to-one correspondence between the collection of right modular groupoids
with a left identity element l and laterally commutative, l-bi-unital
semiheaps. This result is applied to prove that the natural ternary product
induced by a right modular groupoid S with left identity is isomorphic to the
natural ternary product of a groupoid T if and only if S and T are isomorphic
groupoids. Ternary products of other classes of groupoids are also
characterised, including the natural and standard ternary products of inverse
semigroups. These two classes of ternary products are proved to be varieties of
type (3,1,1).
