Volume partition and void spatial distribution in packings of three kinds of Platonic polyhedral granular particles are studied experimentally based on reconstructed three-dimensional packing structures obtained with magnetic resonance imaging techniques. The packing structures are characterized with various structural and topological parameters, and compared with packings of granular spheres. It turns out that the angularity of polyhedral particles strongly affects the global packing fraction of their random close packing states, Voronoi structures and spatial correlations. Meanwhile, the pore size distribution and void connectivity topology are indirectly influenced by the shapes of individual particles, and demonstrate universal dependences on the global packing fraction. Particularly, for the three types of angular and faceted granular particles studied here, the structural differences between icosahedral, dodecahedral and spherical packings are only quantitative, while the octahedral packing displays some qualitatively different structures, implying an upper limit of particle asphericity, below which the results of spherical packing structures can be properly generalized to understand non-spherical granular systems.

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