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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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Murphy et al. (2024) studied this question.
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