Let $P \subseteq \mathbb{R}^d$ be an $\mathcal{H}$-polytope. The *vertex enumeration problem* asks for the set of vertices $V$ of $P$. Theoretically, the vertex enumeration problem for $P$ can be performed in $\mathcal{O}(|V|^{\lfloor d/2 \rfloor})$, cf. [1].
Practically, one would use the *double description method*, cf. [2], and cf. cddlib for an implementation of the former.

In my application, I have to solve a rather large number of such vertex enumeration problems in let's say dimension $10$. Unfortunately, *ccdlib* is too slow and causes numerical problems (the GMP version is even slower).

Moreover, for my application it suffices to find a superset of $V$. Hence, I thought there might be a way to decompose $P$ into "simpler" polytopes such that the vertex enumeration for each such polytope could be performed much faster.

Is anybody aware of such method?