# Third-regular bi-embeddings of Latin squares

Donovan, D. M.; Grannell, M. J. and Griggs, T. S. (2010). Third-regular bi-embeddings of Latin squares. Glasgow Mathematical Journal, 52(3) pp. 497–503.

## Abstract

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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