markoff triples were introduced in 1879 and have a rich history spanning many branches of mathematics. in 2016, bourgain, gamburd, and sarnak answered a long standing question by showing there exist infinitely many composite markoff numbers. their proof relied on showing the connectivity for an infinite family of graphs associated to markoff triples modulo p for infinitely many primes p. in this talk we discuss what happens for the projective analogue of markoff triples, that is surfaces w in $p^1$x$p^1$x$p^1$ cut out by the vanishing of a (2,2,2)-form that admit three non-commuting involutions and are fixed under coordinate permutations and double sign changes. inspired by the work of b-g-s we investigate such surfaces over finite fields, specifically their orbit structure under their automorphism group. for a specific one-parameter subfamily $w_k$ of such surfaces, we construct finite orbits in $w_k(c)$ by studying small orbits that appear in  $w_k$($f_p$) for many values of p and k. this talk is based on joint work with e. fuchs, j. silverman, and a. tran.