Cellular Automorphisms and Self-Duality
We catalog up to a type of reducibility all cellular automorphisms of the sphere, projective plane, torus, Klein bottle, and three-crosscaps (Dyck's) surface. We also show how one can obtain all self-dual embeddings in a surface S given a catalog of all irreducible cellular automorphisms in S.
& Slilaty, D.
(2015). Cellular Automorphisms and Self-Duality. Transactions of the American Mathematical Society, 387 (11), 7695-7773.