  When solving the Poisson equation on honeycomb hexagonal grids, we show that
the $P_1$ virtual element is three-order superconvergent in $H^1$-norm, and
two-order superconvergent in $L^2$ and $L^\infty$ norms. We define a local
post-process which lifts the superconvergent $P_1$ solution to a $P_3$ solution
of the optimal-order approximation. The theory is confirmed by a numerical
test.
