given couple $(w,t)$ clearly only depends on the choice of $w\in \mathsf{H}$. We will then call an element $w\in \mathsf{H}$ non-singular when the inter model sets $\mathfrak{P}(w+ \stackrel{\circ }{W}) -t = \Lambda =\mathfrak{P}(w+ W) -t$ are non-singular. Such a subset of non-singular elements may easily described: it consists of all $w\in \mathsf{H}$ where no point of the subgroup $\Gamma ^*$ of $\mathsf{H}$ enters the boundary $w+\partial W$ of the translated window $w+W$. It thus consists of the complementary subset $$\begin{aligned}
 NS:= \left[ \Gamma ^*-\partial W\right]  ^c\end{aligned}$$ This set is always non-empty from the Baire category theorem, as $W$ was assumed topologically regular, hence with boundary of empty interior in $\mathsf{H}$, and $\Sigma$ (hence $\Gamma ^*$) was supposed to be countable. As already pointed out, the non-singular model sets arising from a common cut $\&$ project scheme with window have a common language, which means that any pattern of some non-singular model set appears elsewhere in all other non-singular model sets. Denoting $\mathcal{L}_{NS}$ this language, we are led to consider its associated *hull*

\[def:hull\] Given a cut $\&$ project scheme and a window, $\mathcal{L}_{NS}$ the language of any non-singular model set arising from this data, the hull of this data is 