  We provide a condition on the links of a polygonal complex X that is
sufficient to ensure Aut(X) has the Haagerup property, and hence so do any
closed subgroups of Aut(X) (in particular, any group acting properly on X). We
provide an application of this work by considering the group of automorphisms
of simply-connected triangle complexes where the link of every vertex is
isomorphic to the graph F090A, as constructed by \'Swi\k{a}tkowski.
