  We present a symmetry-based method for obtaining suitable tensor descriptions
of lattice vertex functions without spinor components. The approach is based on
finding the polynomial functions of vertex momenta, which satisfy the
appropriate tensor transformation laws under hypercubic symmetry
transformations. We use the method to find the most general possible (up to
finite volume effects) basis decompositions for lattice vectors and second-rank
tensors. The leading-order non-continuum versions of these representations are
then applied to the Landau gauge gluon propagator and ghost-gluon vertex of
Monte Carlo simulations, to reveal two interesting insights. First, it is
demonstrated numerically and analytically that there exist special kinematic
configurations where the basis descriptions of both functions reduce to their
continuum analogues. Second, for the gluon two-point correlator it is shown
that the rate at which the function approaches its continuum form in the
infrared is independent of the lattice gauge coupling $\beta$ (when working in
lattice units): the said rate depends on kinematics alone and is ultimately
dictated by the numerical gauge-fixing procedure. We also comment on how this
reflects on the lattice investigations of the anomalous magnetic moment of the
muon. Finally, we argue how our findings can be used to directly test some of
the continuum extrapolation methods.
