Von Gehlen, GPakuliak, SSergeev, Sergey2015-12-130305-4470http://hdl.handle.net/1885/87833We report progress in constructing Boltzmann weights for integrable three-dimensional lattice spin models. We show that a large class of vertex solutions to the modified tetrahedron equation (MTE) can be conveniently parametrized in terms of Nth roots ofTheta-function Parametrization and Fusion for 3D Integrable Boltzmann Weights200410.1088/0305-4470/37/4/0052015-12-12