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Plasmonic nanocavities form very robust sub-nanometer gaps between nanometallic structures and confine light within deep subwavelength volumes to enable unprecedented control of light-matter interactions. However, spherical nanoparticles acquire various polyhedral shapes during their synthesis, which has a significant impact in controlling many light-matter interactions, such as photocatalytic reactions. Here, we focus on nanoparticle-on-mirror nanocavities built from three polyhedral nanoparticles (cuboctahedron, rhombicuboctahedron, decahedron) that commonly occur during the synthesis. Their photonic modes have a very intricate and rich optical behaviour, both in the near- and far-field. Through a recombination technique, we obtain the total far-field produced by a molecule placed within these nanocavities, to reveal how energy couples in and out of the system. This work paves the way towards understanding and controlling light-matter interactions, such as photocatalytic reactions and non-linear vibrational pumping, in such extreme environments.