Biembeddings of Latin squares of side 8

Grannell, Mike; Griggs, Terry and Knor, M. (2007). Biembeddings of Latin squares of side 8. Quasigroups and Related Systems, 15(2) pp. 273–278.

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Abstract

Face 2-colourable triangular embeddings of complete tripartite graphs $K_{n,n,n}$ correspond to biembeddings of Latin squares of side $n$ . We consider biembeddings that contain any of the five Latin squares derived from the Cayley tables of finite groups of order 8. Up to isomorphism, we determine all such biembeddings.