  In this work we propose a discretisation method for the Reissner--Mindlin
plate bending problem in primitive variables that supports general polygonal
meshes and arbitrary order. The method is inspired by a two-dimensional
discrete de Rham complex for which key commutation properties hold that enable
the cancellation of the contribution to the error linked to the enforcement of
the Kirchhoff constraint. Denoting by $k\ge 0$ the polynomial degree for the
discrete spaces and by $h$ the meshsize, we derive for the proposed method an
error estimate in $h^{k+1}$ for general $k$, as well as a locking-free error
estimate for the lowest-order case $k=0$. The theoretical results are validated
on a complete panel of numerical tests.
