[en] The braids R-circumflex, the underlying structure of the Boltzmann weight of the solvable lattice model, are obtained for the fundamental representation of the exceptional quantum group E₆. The symmetry properties of quantum Clebsch-Gordan coefficients and the braids R-circumflex under the Weyl reflection are noted. The fusion matrices of the E₆ WSW models and the link polynomials are constructed. The symmetries of the braids R-circumflex predict the symmetry of the Boltzmann weights of the vertex model based on the E₆. The E₇ and F₄ quantum groups are briefly commented. (author). 11 refs, 2 figs, 1 tab