Donovan, D. M.; Grannell, M. J. and Griggs, T. S.
Third-regular bi-embeddings of Latin squares.
Glasgow Mathematical Journal, 52(3)
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For each positive integer , there is a well-known regular orientable Hamiltonian embedding of , and this generates a regular face 2-colourable triangular embedding of . In the case (mod 8), and only in this case, there is a second regular orientable Hamiltonian embedding of . The current paper presents an analysis of the face 2-colourable triangular embedding of that results from this. The corresponding Latin squares of side are determined, together with the full automorphism group of the embedding.
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