$W$, any inter model set is a *Delone set*, that is to say a uniformly discrete and relatively dense subset of $\mathbb{R}^d$. In fact, it also admits the stronger property of being a *Meyer set*, meaning that any inter model set $\Lambda$ admits a uniformly discrete difference subset $\Lambda - \Lambda$ in $\mathbb{R}^d$. Most of the content of this article is about real cut $\&$ project schemes together with polytopal windows in their internal spaces, hence providing inter model sets which are regular.

Non-singular model sets
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An important notion affiliated with a point pattern $\Lambda$ is its *language*, namely the collection of all ’circular-shaped’ patterns appearing at sites of the point pattern: $$\begin{aligned}
\mathcal{L}_\Lambda := \left\lbrace (\Lambda -\gamma )\cap B(0,R) \, \vert \, \gamma \in \Lambda , \; R> 0\right\rbrace \end{aligned}$$

Not all inter model sets coming from a comon cut $\&$ project scheme and window have same language. However, the class of *non-singular model sets*, also often called *generic model sets*, do share their language:

\[def:non.singular\] A non-singular model set is an inter model set for which we have equalities $$\begin{aligned}
 \mathfrak{P}(w+ \stackrel{\circ }{W}) -t = \Lambda =\mathfrak{P}(w+ W) -t\end{aligned}$$

The situation where such equality occurs for a 