### 3.7.175. Orthotope

A constraint involving orthotopes. An orthotope corresponds to the generalisation of the rectangle and box to the $n$-dimensional case. In addition its sides are parallel to the axes of the Β placement space. FigureΒ 3.7.46 illustrates the notion of orthotope for $n=1,2,3$ and 4. A collection usually named $\mathrm{\pi Ύ\pi \pi \pi ·\pi Ύ\pi \pi Ύ\pi Ώ\pi ΄}$, declared as $\mathrm{\pi Ύ\pi \pi \pi ·\pi Ύ\pi \pi Ύ\pi Ώ\pi ΄}-\mathrm{\pi \pi \pi \pi \pi \pi \pi \pi \pi \pi }\left(\mathrm{\pi \pi \pi }-\mathrm{\pi \pi \pi \pi },\mathrm{\pi \pi \pi £}-\mathrm{\pi \pi \pi \pi },\mathrm{\pi \pi \pi }-\mathrm{\pi \pi \pi \pi }\right)$, defines for each dimension $d$ (with $d\beta \left[1,n\right]$) the coordinate of its lower corner, the size and the coordinate of its upper corner in dimension $d$. FigureΒ 3.7.47 illustrates the representation of an orthotope for $n=2$.