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Quasicrystals: Between Spongy and Full Space Filling

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Diamond and Related Nanostructures

Part of the book series: Carbon Materials: Chemistry and Physics ((CMCP,volume 6))

Abstract

Quasicrystals are structures showing long-range ordering rather than translational periodicity and could be either spongy or filled ones. Spongy structures are hollow-containing materials, encountered either in natural zeolites or in synthesized spongy carbon. Filled structures consist of small cages and/or tiles that can fill a given space. The design and topological study of some hypothetical structures is presented in terms of map operations and genus calculation of their associated graphs, respectively. Among the discussed structures, one remarks some novel spongy hyper-dodecahedra that can evolve with 1 periodicity. Other spherical multi-shell cages represent aggregates of smaller cages, the classical C60 fullerene included. A whole gallery of nanostructures is presented in the Appendices.

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Authors and Affiliations

  1. Faculty of Chemistry and Chemical Engineering, Babes-Bolyai University, 400028, Cluj, Romania

    Mircea V. Diudea

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Editors and Affiliations

  1. Faculty of Chemistry and Chemical Engine, Babes-Bolyai University, Arany Janos street 11, Cluj-Napoca, 400028, Romania

    Mircea Vasile Diudea

  2. , Faculty of Chemistry and Chemical Engine, Babes-Bolyai University, Arany Janos street 11, Cluj-Napoca, 400028, Romania

    Csaba Levente Nagy

Appendices

Appendices

19.1.1 Appendix 19.1. C20 Patterned Structures

Equivalence classes of 20(20)_250

Vertices (250): 5^6 {60}; 5^5 {30; 60}; 5^3 {20; 60; 20}

(given in decreasing centrality, from top to bottom and from left to right, in the figure below)

Edges (450): {60^5; 30; 120}; rings/faces (222): {60^3; 30(tubes); 12 (windows)}

figure 0019a

Vertex equivalence classes of 20(1)(12)(20)_270: 5^6{20; 20; 30; 60}; 5^5 {60}; 5^3 {60; 20}

figure 0019b
figure 0019c
figure 0019d
figure 0019e
figure 0019f

19.1.2 Appendix 19.2. C28 Patterned Structures

figure 0019g
figure 0019h
figure 0019i

19.1.3 Appendix 19.3. Truncated Octahedron 24 = C24 Patterned Structures

figure 0019j
figure 0019k

Truncated Tetrahedron 12 Patterned Structures

figure 0019l
figure 0019m

19.1.4 Appendix 19.4. Penrose-Like 3D Structures: Designed by Dualization of Medials Du(Med(M))

figure 0019n
figure 0019o
figure 0019p
figure 0019q
figure 0019r
figure 0019s

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Diudea, M.V. (2013). Quasicrystals: Between Spongy and Full Space Filling. In: Diudea, M., Nagy, C. (eds) Diamond and Related Nanostructures. Carbon Materials: Chemistry and Physics, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6371-5_19

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