It has recently been discovered than the rutile phase of zinc fluoride shows negative thermal expansion along all three crystallographic axes. What is highly unusual about this material is that its structure consists of edge-sharing ZnF6 octahedra; in every case of a material containing cations and anions that shows negative thermal expansion, the structural polyhedra are connected only at corners. Sharing edges increases significantly the rigidity of the structure, which should mitigate against negative thermal expansion. We propose a total scattering experiment to be analysed by the Reverse Monte Carlo method to understand the nature of the structural fluctuations that lead to negative thermal expansion. To draw good conclusions, we plan also a parallel set of measurements on the rutile phase of titanium dioxide for comparison.