Many interesting target guest molecules have low symmetry, yet most methods for synthesising hosts result in highly symmetrical capsules. Methods of generating lower-symmetry pores are thus required to maximise the binding affinity in host-guest complexes. Here, we use mixtures of tetraaldehyde building blocks to access low-symmetry imine cages. Whether a low-energy cage is isolated can be correctly predicted from the thermodynamic preference observed in computational models. The stability of the observed structures depends on the geometrical match of the aldehyde building blocks. One bent aldehyde stands out as unable to assemble into high-symmetry cages—and the same aldehyde generates low-symmetry socially self-sorted cages when combined with a linear aldehyde. We exploit this finding to synthesise a family of low-symmetry cages containing heteroatoms, illustrating that pores of varying geometries and surface chemistries may be reliably accessed through computational prediction and self-sorting.