Geodesic
On biembedding an idempotent Latin square with its transpose
Acta mathematica Universitatis Comenianae, Tome 82 (2013) no. 1, pp. 11-20 
D. M. Donovan; T. S. Griggs; C. Psomas; D. M. Donovan; T. S. Griggs; C. Psomas. On biembedding an idempotent Latin square with its transpose. Acta mathematica Universitatis Comenianae, Tome 82 (2013) no. 1, pp. 11-20. http://geodesic.mathdoc.fr/item/AMUC_2013_82_1_a1/
@article{AMUC_2013_82_1_a1,
     author = {D. M. Donovan and T. S. Griggs and C. Psomas and D. M. Donovan and T. S. Griggs and C. Psomas},
     title = { On biembedding an idempotent {Latin} square with its transpose},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {11--20},
     year = {2013},
     volume = {82},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2013_82_1_a1/}
}
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Voir la notice de l'article provenant de la source Comenius University

Let L be an idempotent Latin square of side n, thought of as a set of ordered triples (i, j, k) where L(i, j) = k. Let I be the set of triples (i, i, i). We consider the problem of biembedding the triples of L - I with the triples of L' - I, where L' is the transpose of L, in an orientable surface. We construct such embeddings for all doubly even values of n.