Tetrahedral Clusters

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


The first Platonic solid, Tetrahedron, is self-dual; higher dimensional analogues are called simplex/simplices; tetrahedral shapes can be found in vary polyhedral clusters. Adamantane-like structure, Ada20, is a hyper-tetrahedron, a tetrahedron of which points were changed by four tetrahedral units P@4C20; the central hollow has the topology of small fullerene C28; Ada20 is the unit of “diamond D5”, or MTN zeolite. Map operations, like medial m, truncation t and leapfrog l were applied to Ada20, to obtain a variety of spongy or filled structures. Tetrahedral hyper-structures decorated only with dodecahedra were also described. Figure count was used for characterization of the discussed clusters. 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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