Symmetry-type graphs of Platonic and Archimedean solids

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Symmetry-type graphs of Platonic and Archimedean solids

Kovič, Jurij

Mathematical Communications, 12/2011, Volume: 16, Issue: 2

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A recently developed theory of flag-graphs and $k$-orbit maps classifies maps according to their symmetry-type graphs. We propose a similar classification for polyhedra showing that Platonic and Archimedean solids with the same vertex pattern have isomorphic symmetry-type graphs and introducing some tools for the determination of symmetry-type graphs of any polyhedron.

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