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Face embeddings of Archimedean solids

2024/04/23 by Murphy, Tommy, Weed, David
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2404.15142

Abstract

We characterize the Archimedean solids among the convex uniform polyhedra via face embeddings into a regular Tetrahedron. This result has been listed without proof in the literature. As an application, we obtain a lattice packing of ℝ3 by the truncated Icosahedron whose packing density is notably close to the optimal value obtained in [1].

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