Fano plane’s embeddings on compact orientable surfaces

Abstract

In this paper we study embeddings of the Fano plane as a bipartite graph. We classify all possible embeddings especially focusing on those with non-trivial automorphism group. We study them in terms of rotation systems, isomorphism classes and chirality. We construct quotients and show how to obtain information about face structure and genus of the covering embedding. As a by-product of the classification we determine the genus polynomial of the Fano plane.