= Mark B. Villarino
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<Mark B. Villarino> wrote an elementary classification argument for <Archimedean solids> using <Euler formula for a sphere>. His paper proves the thirteen exceptional convex cases, treating <prisms> and <antiprisms> as separate infinite families.<On the Archimedean or Semiregular Polyhedra by Mark B. Villarino>[Original byline, abstract and sections 1.2 and 5]{ref}
The counting argument relates the faces meeting at a vertex to a global constraint on vertices, edges and faces. This makes a short topological identity constrain possible three-dimensional shapes. The classification must specify its convexity and vertex-uniformity assumptions to avoid including different notions of semiregularity.
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