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Tiles from projections of the root and weight lattices of $A_n$
Main purpose of this work is to introduce a general technique of projection of the Voronoi tessellation of the weight lattice $A_n^\ast$ and apply it for the lattice $A_4^\ast$. The projection of the Voronoi tessellation of the weight lattice $A_4^\ast$ produces a totally different tiling scheme tha
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