An interesting case is the Tet 2 4 Di 8 topology, termed a doublewalled tetrahedron. In this instance, there are no stable structures in the whole angle space (see details in Fig. ), and further analysis shows that there is a systematic strain in the structure, which we propose to be due to the required twist in the ditopic building blocks bridging some of the tetratopic sites (this can be seen in known experimental structures of Pd(II) cages in this topology). Therefore, the torsion constraint Under this model, if only a single species is stable at a given point in phase space, we assume that self-sorting will occur and produce only that species. Fig. clearly shows different degrees of self-sorting for 296 topologies with 3-connected and 4-connected building blocks. 297 This is summarised clearly in Fig. , where the percent-298 age of selected systems is higher for 4-connected cages than 299 3-connected cages (under the rigid regime) and remains sig-300 nificant up to higher energy thresholds. It is possible that 301 including all enumerated topologies, as in the work by Poole et 302 al. may alter this behaviour. Fig. shows that the number 303 of unstable cages is higher for the 4-connected topologies than 304 the 3-connected topologies. This outcome, from our very sim-305 ple model, suggests that 3-connected topologies, at least with 306 symmetric tritopic building blocks, will suffer from more com-307 petition during self-assembly than the 4-connected topologies. 308 We also show that the self-sorting propensity depends on the 309 pyramidal angles of the tritopic or tetratopic building block, 310 where planar building blocks lead to more selected isomers at 311 higher energy thresholds (Fig. ). Focusing on the smallest, 312 stable topology, Fig. and Fig. show regions of stability 313 for most topologies, where the largest topologies tend to be 314 favoured at larger internal angles. Therefore, it is possible to design for a particular cage topology if desired. Regarding selection, Fig. shows that the percentage of 338 selected cage structures decreases significantly when preorgani-339 sation is switched off. A geometrical effect of removing this 340 torsion restriction on the cage structures is shown in Fig. ,