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An $i$-packing in a graph $G$ is a set of vertices at pairwise distancegreater than $i$. For a nondecreasing sequence of integers$S=(s\_{1},s\_{2},\ldots)$, the $S$-packing chromatic number of a graph $G$ isthe least integer $k$ such that there exists a coloring of $G$ into $k$ colorswhere each set of vertices colored $i$, $i=1,\ldots, k$, is an $s\_i$-packing.This paper describes various subdivisions of an $i$-packing into $j$-packings($j\textgreater{}i$) for the hexagonal, square and triangular lattices. Theseresults allow us to bound the $S$-packing chromatic number for these graphs,with more precise bounds and exact values for sequences $S=(s\_{i},i\in\mathbb{N}^{*})$, $s\_{i}=d+ \lfloor (i-1)/n \rfloor$.

Subdivision into i-packings and S-packing chromatic number of some lattices