We generated 2890 cages in our cage space from a pool of 287 159 distinct building block combinations and 13 topologies, with 160 and without torsion restriction. We explored the effect of cage 161 topology, building block coordination number, building block 162 flexibility and target internal angles of the two building blocks 163 on topology accessibility relationships and approximations to 164 self-sorting behaviour (Fig. ). Note that the cage space is dis-165 cretised over the target internal angle values, which are shown 166 in all plots. We implemented an optimisation sequence, de-167 scribed in Section S3, that is reasonably robust, but does result 168 in some instabilities in the phase space (Section S5). However, 169 we show that the optimised cage models have structural pa-170 rameters that match the input force field parameters and that 171 most of the strain exists in the angle terms (Section S4). ). This outcome, again, is consistent with the geometry of a tetrahedron. What is less obvious is why there are stable points at low internal angles for smaller tritopic angles (structures 1-3 in Fig. ). We posit that these structures are geometrically stable in the framework of this model, but may be difficult to realise using real chemical structures. However, this highlights new geometries that we could target in future design studies based on our models.