Why are there only 13 Archimedean solids and not 14?

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I just finished a project on solids for geometry and I couldn’t help but wonder out of curiosity why are there only 13 Archimedean solids and not 14 or more?

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This question has been answered in this publication : Walsh, T. R. S. ``Characterizing the Vertex Neighbourhoods of Semi-Regular Polyhedra.'' Geometriae Dedicata 1, 117-123, 1972. link