The discretisation theorem we introduced is implemented as a method to partition the configuration space into regions of contiguous generic symmetry. A worked example using a triangular segment of the configuration space from Fig. is shown in Fig. . This 2-dimensional curved configuration space is composed of the central 2-dimensional region (greencoloured) corresponding to polytopes of D2 generic symmetry, bounded by the 1-dimensional line segment regions (red coloured) of D2h and D2d generic symmetries as indicated. These line segments are in turn bounded by the zero-dimensional points (blue coloured) of Td, D4h, and Dh generic symmetries as indicated. These zero-dimensional points also complete the full boundary of the 2D triangular region at its vertices (corners).