  The majority of viruses are organised according to the structural blueprints
of the seminal Caspar-Klug theory. However, there are a number of notable
exceptions to this geometric design principle. Prominent examples are the
cancer-causing papilloma viridae and the \textit{de novo} designed AaLS cages
that exhibit non-quasiequivalent capsid structures with protein numbers
excluded by Caspar-Klug theory. The biophysical properties of these
geometrically distinct architectures and the fitness advantages driving their
evolution are currently unclear. We investigate here the resilience to
fragmentation and disassembly behaviour of these capsid geometries by
introducing a percolation theory on weighted graphs. We show that these cage
architectures follow one of two distinct disassembly pathways, preferring
either hole formation or capsid fragmentation. This suggests that preference
for specific disassembly scenarios could be a driving force for the evolution
of the non Caspar-Klug protein container architectures.
