Trigonometric and Ssub(N)-symmetric solutions of triangle equations with variables on the faces

General properties of triangle equations with variables on faces are discussed. The solution of triangle equations is a main point for study of different problems in quantum mathematical physics. A simple method to search for the solutions of these equations is offered. The statistical vertex model is formulated. The unitarity and crossing symmetry conditions are derived. Solutions of triangle equations for Ssub(N)-symmetric model are obtained