  A branched covering $f: S^2 \to S^2$ is a nearly Euclidean Thurston (NET) map
if each critical point is simple and its postcritical set has exactly four
points. We show that up to equivalence, each NET map admits a normal form in
terms of simple affine data. This data can then be used as input for algorithms
developed for the computation of fundamental invariants, now systematically
tabulated in a large census.
