No strongly regular graph is locally Heawood

We investigate when a strongly regular graph is locally Heawood. We focus on a putative strongly regular graph with parameters $(v, k, \lambda, \mu) = (85, 14, 3, 2)$, which is the only candidate for such a graph. Assuming that the graph is locally Heawood, we analyze its structure, finally arriving to a contradiction, which allows us to conclude that no strongly regular graph is locally Heawood.