  The paths on the {\bf R$^3$} real Euclidean manifold are defined as
2-dimensional simplicial strips; points are replaced by 2-simplexes and the
orbits of the action of a one discrete-parameter group on the base manifold
becomes a convex polyhedron attached to a 2-dimensional simplicial complex. The
Lagrangian of a moving mass is proportional to the width of the path. The
special relativistic form of the Lagrangian is recovered in the continuum
limit, without relativistic Lorenz invariance considerations.
