  In J. Sci. Comput., 81: 2188-2212, 2019, we considered a superconvergent
hybridizable discontinuous Galerkin (HDG) method, defined on simplicial meshes,
for scalar reaction diffusion equations and showed how to define an
interpolatory version which maintained its convergence properties. The
interpolatory approach uses a locally postprocessed approximate solution to
evaluate the nonlinear term, and assembles all HDG matrices once before the
time intergration leading to a reduction in computational cost. The resulting
method displays a superconvergent rate for the solution for polynomial degree
$k\ge 1$. In this work, we take advantage of the link found between the HDG and
the hybrid high-order (HHO) methods, in ESAIM Math. Model. Numer. Anal., 50:
635-650, 2016 and extend this idea to the new, HHO-inspired HDG methods,
defined on meshes made of general polyhedral elements, uncovered therein}. We
prove that the resulting interpolatory HDG methods converge at the same rate as
for the linear elliptic problems. Hence, we obtain superconvergent methods for
$k\ge 0$ by some methods. We present numerical results to illustrate the
convergence theory.
