Operations on Maps

  • Mircea Vasile Diudea
Part of the Carbon Materials: Chemistry and Physics book series (CMCP, volume 10)


Design of structures discussed in this book is based on “operations on maps” (topological-geometrical modifications of a parent map), merely applied on the Platonic solids: tetrahedron (T), cube (C), octahedron (O), dodecahedron (D) and icosahedron (I); a map M is a discretized surface domain. The operations discussed in the Chap.  2 are: dual d, medial m, truncation t, polygonal mapping p n , snub s, leapfrog l, quadrupling/chamfering q, and septupling/wirl s n .

The figure sequence of a modified polyhedron: {v, e, f}, is given function of the edges e of the parent polyhedron; all the parameters herein presented refer to regular maps. The symmetry of parents is preserved by running these operations. An Atlas of single-shell clusters derived from the Platonic solids is also presented.


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© Springer International Publishing AG 2018

Authors and Affiliations

  • Mircea Vasile Diudea
    • 1
  1. 1.Department of Chemistry, Faculty of Chemistry and Chemical EngineeringBabes-Bolyai UniversityCluj-NapocaRomania

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