where helicity occurs without torsion restrictions, which is akin 342 to recent work in Pd2L4 cages. Further, we see that there For small ditopic internal angles, removing the torsion re-351 striction has a strong impact, resulting in many low energy 352 cages in the angle map (Fig. ). This results in more mixing in the accessible topology maps (Section S10) than in the restricted case. Focusing on the smallest accessible topology at each point, the topology maps show that the preferred topology shifts from the smallest to the largest topology as the internal angles increase with unstable regions in the top-right-hand corner. However, this is not the case when preorganisation is on. Further, different topologies are preferred (as the smallest stable structure) with and without torsion restrictions for a given pair of building block pairs. There are regions that were unstable or favoured larger topologies, that now favour smaller topologies when preorganisation is not present. As expected for such a minimal model, the effect of preorganisation is negligible at higher internal angles, where the torsion has a smaller effect. Fig. (b) summarises the change in the proportion of accessible structures with and without restricted torsions. The difference between topologies with 3-connected and 4-connected building blocks is interesting; the effect of preorganisation on topology stability is much more variable for 3-connected topologies. However, this could be a feature of the studied topologies, not the connectivity. For example, the Tet 2 Di 8 topology ignores this trend (all restricted cages are deemed unstable in our model; see above). The change in accessibility of a given topology due to flexibility (the gap between white and blue bars in Fig. (b), larger gaps suggest larger effect of flexibility) may be a useful indicator of the degree of difficulty of the rational design of a certain topology with flexible components. Our model does not consider the free energy or varying flexibility within cage bonds and angles, all of which would significantly impact the self-sorting of flexible structures. Overall, the role of flexibility will diminish the effectiveness of geometry-based design principles, and our data shows that it increases the competition between different cage topologies. However, it is not immediately clear whether these results are false positives due to the model's simplicity. Regardless, simple models such as this can begin to uncover where and how to introduce flexibility in the most useful and robust way, avoiding the pitfalls of challenging synthetic outcomes and optimising materials properties. 3.4. Relationship between building blocks, shape and topology. The shape of cage molecules determines the properties of their intrinsic pores and influences their packing behaviour. As defined, 9,10 the topology of a cage molecule does not necessarily provide information on the eventual cage geometry. Here, we systematically mapped the relationship between topology, shape and building block parameters. We calculate a series of shape measures for a given cage structure, which are the deviation of that cage from ideal shapes, using the SHAPE v2.1 software. We calculate the shape only for some topologies (shapes with vertex numbers 3 to 8 to avoid the cost of 12-vertex calculations), and we do so on the centroids of either the tritopic/tetratopic building blocks or the ditopic building blocks in the cage structure. For example, for the Tri 4 Di 6 topology, we calculate the shapes based on the positions of the four tritopic building blocks (compared to four-vertex shapes, e.g., square and tetrahedron) and based on the positions of the six ditopic building blocks (compared to six-vertex shapes, e.g., octahedron). Therefore, some topologies will have two shape measures (more detail in Section S11). Table shows the ideal shape of each topology, where the naming convention states the geometry and the number of vertices in the shape deviation measure. Importantly, these deviation measures are unitless and allow quantitative comparison between different shapes.