Using a modified version of the tetrahedron equations we construct a new family of N- state three-dimensional integrable models with commuting two-layer transfer matrices. We investigate a particular class of solutions to these equations and parametrize them in terms of elliptic functions. The corresponding models contain one free parameter, k—an elliptic modulus.
BOOS, HE., Mangazeev, V. V., & SERGEEV, S. (1995). MODIFIED TETRAHEDRON EQUATIONS AND RELATED 3D INTEGRABLE MODELS , I. International Journal of Modern Physics A, 10(28), 4041-4063. https://doi.org/10.1142/S0217751X9500187X