  We prove that, in the limit as $k \to+ \infty$, the hexagonal honeycomb
solves the optimal partition problem in which the criterion is minimizing the
largest among the Cheeger constants of $k$ mutually disjoint cells in a planar
domain. As a by-product, the same result holds true when the Cheeger constant
is replaced by the first Robin eigenvalue of the Laplacian.
