Panel structures of triangulations on the torus

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.