  We shall interpret the null hexagonal Wilson loop (or, equivalently, six
gluon scattering amplitude) in 4D ${\cal N}=4$ Super Yang-Mills, or, precisely,
an integral representation of its matrix part, via an ADHM-like instanton
construction. In this way, we can apply localisation techniques to obtain
combinatorial expressions in terms of Young diagrams. Then, we use our general
formula to obtain explicit expressions in several explicit cases. In
particular, we discuss those already available in the literature and find exact
agreement. Moreover, we are capable to determine explicitly the denominator
(poles) of the matrix part, and find some interesting recursion properties for
the residues, as well.
