  R. Lawrence and D. Sullivan have constructed a Lie model for an interval from
the geometrical idea of flat connections and flows of gauge transformations.
Their model supports an action of the symmetric group $\Sigma_2$ reflecting the
geometrical symmetry of the interval. In this work, we present a Lie model of
the triangle with an action of the symmetric group $\Sigma_3$ compatible with
the geometrical symmetries of the triangle. We also prove that the model of a
graph consisting of a circuit with $k$ vertices admits a Maurer-Cartan element
stable by the automorphisms of the graph.
