  There are many examples of several-variable polynomials whose Mahler measure
is expressed in terms of special values of polylogarithms. These examples are
expected to be related to computations of regulators, as observed by Deninger,
and later Rodriguez-Villegas, and Maillot. While Rodriguez-Villegas made this
relationship explicit for the two variable case, it is our goal to understand
the three variable case and shed some light on the examples with more
variables.
