We have explored the relationship between internal building block angles and cage internal energy for all topologies in this work (Section S6 and Section S7). The number of stable regions (or wells) and the smoothness in these angle maps tends to increase as the degrees of freedom increase (i.e., for larger topologies). Although, some of the larger topologies do not have this effect. Also, some topologies show two stable wells for a given pyramid angle, for example, at tritopic angle 110 ∘ in Fig. , that deviate from the single well for the planar tritopic or tetratopic case. Visualising structures in these types of surfaces, we see structures with inverted tetratopic or tritopic building blocks as in Fig. (c) 1-3. For other topologies, we see that there are low energy structures up until some critical internal ditopic angle that leads to instability (Fig. , Fig. ). This shows that there are topological effects determining the energy surface associated with these two types of internal angles. The observed topological dependence is non-trivial and may be related to some inherent flexibility. Given the geometrical nature of our approach, it is promising that our models agree with literature examples, e.g., from Ref. 51 and their findings of stable angle-topology combinations in metal-organic polyhedra (they performed a detailed review of the angles in building block pairs and their eventual topology).