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In blast furnaces, burden topography and packing density affect the stability of the burden, permeability of gas flow as well as the heat transfer efficiency. A fundamental understanding of the influence and interaction of coke and ore particles on the burden topography and packing density is therefore essential, in particular the influence of particle shape polydispersity and particle size polydispersity. In this paper we analyze the effect of particle shape and size polydispersity on the coke and ore charge distribution inside a bell-less blast furnace using the discrete element method (DEM). We first validate experimentally the polyhedral particle model with a simplified lab-scale charging experiment. A comparative study between spheres, with rolling friction to account for shape, and polyhedra is conducted for shape and size polydisperse particle systems. It was found that shape polydispersity mainly influenced the topography of the burden, whereas the size polydispersity mainly influenced the inter-layer percolation, i.e. localized particle diffusion, hence the local spatial packing density. The differences between the spherical particle models and polyhedral particle models on the burden topography are also quantitatively and qualitatively presented, especially on the role of particle shape on the push-up of coke in the centre. This study demonstrates that modelling particle shape effects using spheres with rolling friction is insufficient to fully describe the complex behaviour of shaped particles in a blast furnace, as the particle shape has a noteworthy influence on the burden characteristics.