Abstract Equations of motion for a classical 3 d discrete model, whose auxiliary system is a linear system, are investigated. The Lagrangian form of the equations of motion is derived. The Lagrangian variables are a triplet of `tau functions'. The equations of motion for the triplet of tau functions are three trilinear equations. Simple solitons for the trilinear equations are given. Both the dispersion relation and the phase shift reflect the triplet structure of equations.