we've had some discussions here in the past about the wordiness of the verb orientate.

I've had the fortune to stuble upon a parallel formulation in the verb to permutate = to permute. although obviously enough stemming from L. permutare, OED2 suggests perh. after PERMUTATION.

Google[Books] suggests a usage ratio of 24 to 1, so probly at least an order of magnitude in real life.

there are 50 books which have both permute and permutate, including this exceedingly odd looking find:

(iii) For each edge, permutate the two neighboring faces f[l],f[r]
(iv) For each edge, permute the edge attributes "convex" and "concave"