Abstract
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.
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Chapter 8 Atlas: Tetrahedral Clusters
Chapter 8 Atlas: Tetrahedral Clusters
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P@T.5_2 | P@T.5_3 | T.4 |
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T.4 | O.6 | mTP.10=T@O.10 |
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T@(4mP3;4hC)@(mTT).22 | C@(4T;4hC;6mP3)@(mTT).26 | T@O.10=mTP.10 |
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O@(4P3;4hCO)@TT.18 | TT@(4O;4hCO;6P3)@CO.24 | T@4O@O.10=mTP.10 |
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Tr(T)=TT_12 | Tr(Oct)=TO_24 | P3@(3TO;2TO;5TT;9P3).60 |
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l(T@4O@O).90_2 | l(T@4O@O).90_3 | T@4O@O.10=mTP.10 |
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T.4 | TT.12 | tTP.20_3 |
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T.4 | TT.12 | T@TT.16_3 |
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m(T@TT16).36_2 | m(T@TT16).36_3 | mCO.24 |
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T.4 | C20 (I h ) | C28 (T d ) |
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I.12 | Ada20.198 | d(Ada20.198).162 |
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C84 T d =lC28 | (TO@4TO)@(4C60;6P5).264_3 | C960 |
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TO@(4C60;6P5).240_3 | (TO@4TO)@(4C60;6P5).264_3 | C1212 |
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T.4 | ID.30 | Ada20.198 |
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t(C20) | t(C28) | Ada20.198 |
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C84 T d =lC28 | (TT@4TT)@(4C60).210 | C810 |
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Ada20.198 | (TT@4TT)@(4C60).210 | C834 |
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C84 T d =lC28 | 2TT@3C60.165 | Ada20.158 |
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2TT@3C60.165 | TTY(4C165);f 5).630 | C654 |
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t sel (p 4T).22 | s2T.28 | t sel (p 4T)@s 2T.50 |
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D.20 | t sel (p 4T).22 | t sel (p 4T)@s 2T.50 |
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C50_2 | C50_3 | C50_4 |
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d(C50).42_2 | d(C50).42_3 | d(C50).42_4 |
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m(C50).90_2 | m(C50).90_3 | m(C22).36 |
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t(C22).72 | t(C50).180_3 | t(C50).180_4 |
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T.4 | C12 6(3.5.5).6(5.5.5) | D.20 |
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t(C54).200_2 | t(C54).200_3 | t(T@C22).92 |
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Diudea, M.V. (2018). Tetrahedral Clusters. In: Multi-shell Polyhedral Clusters. Carbon Materials: Chemistry and Physics, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-64123-2_8
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DOI: https://doi.org/10.1007/978-3-319-64123-2_8
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