here in nonlocality distillation. That is, starting with two copies with a certain degree of nonlocality we want that the final wired correlation has a higher nonlocality degree. For that, we first have to define a quantifier. Different measures have been considered before, the violation of the CHSH inequality itself [@forster] and the so called EPR-$2$ decomposition [@PhysRevLett.106.020402]. Here we employ the trace distance measure introduced in [@PhysRevA.97.022111], basically quantifying the minimum distance of the nonlocal point in question to the set of local correlations. In the CHSH scenario the trace distance quantifier has been shown to be equivalent to the CHSH inequality violation (up to a constant factor), reason why we consider here as a quantifier $NL(p)$ of the nonlocality of a given distribution $p=p(ab\vert xy)$ the following quantity: $$NL(p)=
            \max\left[ \frac{\Pi(\mathrm{CHSH})-2}{2}, 0 \right]$$ where $\Pi(CHSH)$ stand for all eight simmetries of the CHSH inequality, thus bounding $NL=0$ for local points and $NL=1$ for the PR-box and its symmetries (maximal nonlocality).

Faces of the nonlocal set and quantum voids {#nlsimplex .unnumbered}
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Following [@PhysRevA.99.032106], we represent a probability distribution $p(ab\vert xy)$ as a vector $(p_1,p_2,...,p_{16})$, where the ordering of probabilities is as shown in Table \[tab2\].

On considering the 