  Rips complexes are important structures for analyzing topological features of
metric spaces. Unfortunately, generating these complexes constitutes an
expensive task because of a combinatorial explosion in the complex size. For
$n$ points in $\mathbb{R}^d$, we present a scheme to construct a
$3\sqrt{2}$-approximation of the multi-scale filtration of the $L_\infty$-Rips
complex, which extends to a $O(d^{0.25})$-approximation of the Rips filtration
for the Euclidean case. The $k$-skeleton of the resulting approximation has a
total size of $n2^{O(d\log k)}$. The scheme is based on the integer lattice and
on the barycentric subdivision of the $d$-cube.
