  We present a computational study of smooth curves of degree six in the real
projective plane. In the Rokhlin-Nikulin classification, there are 56
topological types, refined into 64 rigid isotopy classes. We developed software
that determines the topological type of a given sextic and used it to compute
empirical probability distributions on the various types. We list 64 explicit
representatives with integer coefficients, and we perturb these to draw many
samples from each class. This allows us to explore how many of the bitangents,
inflection points and tensor eigenvectors are real. We also study the real
tensor rank, the construction of quartic surfaces with prescribed topology, and
the avoidance locus, which is the locus of all real lines that do not meet a
given sextic. This is a union of up to 46 convex regions, bounded by the dual
curve.
