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Note on ordering and complexity of Platonic and Archimedean polyhedra based on solid angles

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Abstract

The missing values for the solid angles of the two snub semiregular polyhedra have been calculated, and integrated into the whole series of Platonic and Archimedean polyhedra. This is the only criterion which so far gives an unambiguous answer (without any degeneracy leading to posets) on how to order these polyhedra according to their increasing complexity.

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Authors and Affiliations

  1. Department of Mathematics, University of Split, Nikole Tesle 12, 21000, Split, Croatia

    Damir Vukičević

  2. Texas A&M University at Galveston, 5007 Avenue U, Galveston, TX, 77551, USA

    Alexandru T. Balaban

Authors
  1. Damir Vukičević
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  2. Alexandru T. Balaban
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Correspondence to Alexandru T. Balaban.

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Vukičević, D., Balaban, A.T. Note on ordering and complexity of Platonic and Archimedean polyhedra based on solid angles. J Math Chem 44, 725–730 (2008). https://doi.org/10.1007/s10910-008-9361-z

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  • DOI: https://doi.org/10.1007/s10910-008-9361-z

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