Modified Tetrahedron Equations and Related 3D Integrable Models
  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 parameterize them in terms of elliptic functions. The corresponding models contain one free parameter $k$ -- an elliptic modulus. 
H.E. Boos, V.V. Mangazeev, S.M. Sergeev