The paper presents an algorithm for the construction of an approximation of a highly nonlinear current-flux characteristic of a synchronous reluctance machine. Such an approximation is required in a Hamiltonian model of an electric machine and the constructed approximation is suited to be used in such a model. It employs a simplicial approximation based on irregular points sets in the spaces of currents and fluxes. The sets are constructed by the iterative insertion of new points. Initially the sets contain an arbitrarily small number of elements. The insertion is based on an approximation error calculation. Based on the sets containing possibly small number of elements, the proposed procedure leads to smooth and precise approximation. Due to the nonlinearity of the approximated characteristics, ambiguities can occur. A method for the triangulation refinement of the sets of currents and fluxes that eliminates them is also presented. In the paper, a reluctance machine model using the constructed approximation is described and compared with a model using the approximation based on regular sets.