Small Icosahedral Clusters

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


In geometry, any polyhedron with 12 faces is named a dodecahedron, among which only one is the regular dodecahedron (i.e. the Platonic solid), composed of 12 regular pentagonal faces, 3 of which meeting at each vertex; it has the Schläfli symbol {5,3} and icosahedral (point group) symmetry, I h . The dual of a dodecahedron is an icosahedron, referring to shapes, if one disregards the angles and bond length, rather than to regular polyhedra. The fifth chapter shows the transforming, by map operations, of small seeds, like “point centered polyhedra” and “cell-in-cell”, into more complex multi-shell clusters, of rank 4 or 5. Among the transformed polyhedra, a special attention was given to rhombic polyhedra, obtained by the sequence d(m(P)) (i.e. dual of medial polyhedra). An atlas section illustrates the discussed multi-shell polyhedral clusters.

Supplementary material


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Copyright information

© 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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