The {\em Computational Geometry Algorithms Library} {\sc Cgal} currently provides packages to compute triangulations in $\mathbb{R}^2$ and $\mathbb{R}^3$. In this paper we describe a new design for the 3D triangulation package that permits to easily add functionality to compute triangulations in other spaces. These design changes have been implemented, and validated on the case of the periodic space $\T^3$. We give a detailed description of the realized changes together with their motivation. Finally, we show benchmarks to prove that the new design does not affect the efficiency.