Applying the notions called the panel structure and the paneled triangulation introduced by Negami et al. [Re-embedding structures of triangulations on closed surfaces, Sci. Rep. Yokohama Nat. Univ. Sect. I, Math. Phys. Chem. 44 (1997) 41-55], we determine all the numbers of inequivalent embeddings of triangulations on the torus, namely 1-6, 8, 10, 12, 14, 16, 24, 48 and 120. © 2005 Elsevier B.V. All rights reserved.
Sasao, A. (2005). Panel structures of triangulations on the torus. In Discrete Mathematics (Vol. 303, pp. 186–208). https://doi.org/10.1016/j.disc.2005.01.011