. . . But I must speak again about crystals, shapes, colors. There are crystals as huge as the colonnade of a cathedral, soft as mould, prickly as thorns; pure, azure, green, like nothing else in the world, fiery black; mathematically exact, complete, like constructions by crazy, capricious scientists, or reminiscent of the liver, the heart . . . There are crystal grottos, monstrous bubbles of mineral mass, there is fermentation, fusion, growth of minerals, architecture and engineering art ... Even in human life there is a hidden force towards crystallization. Egypt crystallizes in pyramids and obelisks, Greece in columns; the middle ages in vials; London in grinny cubes . . . Like secret mathematical flashes of lightning the countless laws of construction penetrate the matter. To equal nature it is necessary to be mathematically and geometrically exact. Number and phantasy, law and abundance—these are the living, creative strengths of nature; not to sit under a green tree but to create crystals and to form ideas, that is what it means to be at one with nature!


Coordination Number Rock Salt Close Packing Molecular Crystal Molecular Packing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [9-1]
    K. Čapek, Anglické Listy, Československý Spisovatel, Prague (1970).Google Scholar
  2. [9-2]
    P. C. Ritterbush, Nature (London) 301, 197 (1983).CrossRefGoogle Scholar
  3. [9-3]
    A. L. Mackay, Nature (London) 301, 652 (1983).CrossRefGoogle Scholar
  4. [9-4]
    E. Schröder, Dürer, Kunst und Geometrie, Akademie Verlag, Berlin (1980).Google Scholar
  5. [9-5]
    B. Ernst, The Magic Mirror of M. C. Escher, Ballantine Books, New York (1976).Google Scholar
  6. [9-6]
    J. Lima-de-Faria (ed.), Historical Atlas of Crystallography, Kluwer, Dordrecht (1990).Google Scholar
  7. [9-7]
    R. J. Haüy, Traité de Cristallographie, Bachelier et Huzard, Paris (1822). [Reprinted by Culture et Civilisation, Brussels (1968).]Google Scholar
  8. [9-8]
    J. Kepler, Strena seu de nive sexangula, Godefridum Tampach, Frankfurt am Main (1611). [English translation, The Six-Cornered Snowflake, Clarendon Press, Oxford (1966).]Google Scholar
  9. [9-9]
    J. Dalton, Manchester Memoirs 6 (1805).Google Scholar
  10. [9-10]
    C. J. Schnecr, Am. Sci. 71, 254 (1983).Google Scholar
  11. [9-11]
    A. L. Mackay, Izv. Jugosl. Cent. Kristallogr. 10, 15 (1975).Google Scholar
  12. [9-12]
    L. A. Shuvalov, A. A. Urosovskaya, I. S. Zheludev, A. V. Zaleskii, S. A. Semiletov, B. N. Grechushnikov. I. G. Chistyakov, and S A. Pikin, Sovremennaya Kristallografiya, Vol. 4, Fizicheskie Svoistva Kristallov, Nauka, Moscow (1981).Google Scholar
  13. [9-13]
    K. N. Trueblood, in Accurate Molecular Structures. Their Determination and Importance (A. Domenicano and 1. Hargittai, eds.), p. 199, Oxford University Press, Oxford (1992); C. M. Gramaccioli, ibid., p. 220.Google Scholar
  14. [9-14]
    A. L. Mackay, The Floating World of Science, Poems, The RAM Press, London (1980).Google Scholar
  15. [9-15]
    M. J. Buerger, Elementary Crystallography, An Introduction to the Fundamental Geometrical Features of Crystals, 4th printing, John Wiley & Sons, New York (1967);. E. S. Dana, A Textbook of Mineralogy, 4th ed. (revised and enlarged by W. E. Ford), John Wiley & Sons, New York (1932); P. M. Zorky, Arkhilektura Kristallov. Nauka, Moscow (1968).Google Scholar
  16. [9-16]
    Gy. Lengyel, Kézimunkák, Kossuth, Budapest (1978).Google Scholar
  17. [9-17]
    L. V Azaroff, Introduction to Solids, McGraw-Hill (1960).Google Scholar
  18. [9-18]
    International Tables for X-Ray Crystallography, 3rd ed., Kynoch Press, Birmingham, England (1969).Google Scholar
  19. [9-19]
    A. V. Shubnikov and V. A. Koptsik, Symmetry in Science and Art, Plenum Press, New York (1974). [Russian original: Simmetriya v nauke i iskusstve, Nauka, Moscow (1972).]Google Scholar
  20. [9-20]
    C. P. Brock and E. C. Lingafelter, J. Chem. Educ. 57, 552 (1980).CrossRefGoogle Scholar
  21. [9-21]
    A. L. Mackay, Acta Crystallogr. 22, 329 (1967).CrossRefGoogle Scholar
  22. [9-22]
    A. I. Kitaigorodsky, Molecular Crystals and Molecules, Academic Press, New York (1973). [Russian original: A. I. Kitaigorodskii, Molekulyarnie Kristalli, Nauka, Moscow (1971).]Google Scholar
  23. [9-23]
    A. D. Mighell, V. L. Himes, and J. R. Rodgers, Acta Crystallogr., Sect. A 39, 737 (1983); J. Donohue, Acta Crystallogr., Sect. A 41, 203 (1985); R. Srinivasan, Acta Crystallogr, Sect. A 47, 452 (1991); C. P. Brock and J. D. Dunitz, Acta Crystallogr., Sect. A 47. 854 (1991); A. J. C. Wilson, ACH—Models in Chemistry 130, 183 (1993); C. P. Brock and J. D. Dunitz, Mol. Cryst. Liq. Cryst. 242, 61 (1994).Google Scholar
  24. [9-24]
    J. Dalton, A New System of Chemical Philosophy, Manchester, England (1808), p. 128, plate III. Google Scholar
  25. [9-25]
    D. Hodgkin, Kristallografiya 26, 1029 (1981).Google Scholar
  26. [9-26]
    A. F. Wells, Structural Inorganic Chemistry, 5th ed., Clarendon Press, Oxford (1984).Google Scholar
  27. [9-27]
    K. W. Adolph, D. L. D. Caspar, C. J. Hollingshed, E. E. Lattman, W. C. Phillips, and W. T. Murakami, Science 203, 1117 (1979).PubMedCrossRefGoogle Scholar
  28. [9-28]
    R. B. Fuller, Synergetics: Explorations in the Geometry of Thinking, Macmillan, New York (1975), p. 37.Google Scholar
  29. [9-29]
    D. L. D. Caspar and A. Klug, Cold Spring Harbor Symp. Quant. Biol. 27, 1 (1962).PubMedGoogle Scholar
  30. [9-30]
    R. E. Benfield and B. F. G. Johnson, J. Chem. Soc., Dalton Trans. 1980, 1743.Google Scholar
  31. [9-31]
    A. L. Mackay, Acta Crystallogr. 15, 916 (1962).CrossRefGoogle Scholar
  32. [9-32]
    B. C. Chakoumakos, R. J. Hill, and G. V. Gibbs, Am. Mineral. 66, 1237 (1981).Google Scholar
  33. [9-33]
    I. El-Said and A. Parman, Geometric Concepts in Islamic Art, World of Islam Festival Publ. Co., London (1976).Google Scholar
  34. [9-34]
    Chen Chi-Lu, Material Culture of the Formosan Aborigines, The Taiwan Museum, Taipei (1968).Google Scholar
  35. [9-35]
    L. Pauling, The Nature of the Chemical Bond, 3rd ed., Cornell University Press, Ithaca, New York (1973).Google Scholar
  36. [9-36]
    W. Barlow, Z. Kristallogr. 29, 433 (1898).Google Scholar
  37. [9-37]
    J. Bernstein, in Accurate Molecular Structures. Their Determination and Importance (A. Domenicano and I. Hargittai, eds.), p. 469, Oxford University Press, Oxford (1992).Google Scholar
  38. [9-38]
    A. I. Kitaigorodsky, in Advances in Structure Research by Diffraction Methods, Vol. 3 (R. Brill and R. Mason, eds.), p. 173, Pergamon Press, Oxford, and Friedr. Vieweg and Sohn, Braunschweig (1970).Google Scholar
  39. [9-39]
    F. Wundl and E. T. Zellers, J. Am. Chem. Soc. 102, 4283 (1980).CrossRefGoogle Scholar
  40. [9-40]
    F Wundl and E. T. Zellers, J. Am. Chem. Soc. 102, 5430 (1980).CrossRefGoogle Scholar
  41. [9-41]
    C. H. MacGillavry, Symmetry Aspects of M. C. Escher’s Periodic Drawings, Bohn, Scheltema & Holkema, Utrecht (1976).Google Scholar
  42. [9-42]
    P. M. Zorky, ACH—Models in Chemistry 130, 173 (1993).Google Scholar
  43. [9-43]
    H. A. Stuart, Phys. Z. 35, 990 (1934); H. A. Stuart, Z. Phys. Chem. 27, 350 (1934); G. Briegleb, Fortschr. Chem. Forsch. 1, 642 (1950).Google Scholar
  44. [9-44]
    A. Gavezzotti and G. R. Desiraju, Acta Crystallogr., Sect. B 44, 427 (1988).CrossRefGoogle Scholar
  45. [9-45]
    J.-M. Lehn, Science 260, 1762 (1993).PubMedCrossRefGoogle Scholar
  46. [9-46]
    G. D. Andreetti, A. Pochini, and R. Ungaro, J. Chem. Soc., Perkin Trans. 2 1983, 1773; G. D. Andreetti and F. Ugazzoli, in Calixarenes: A Versatile Class of Macrocyclic Compounds (J. Vicens and V. Böhmer, eds.), Kluwer, Dordrecht (1991).Google Scholar
  47. [9-47]
    J.-M. Lehn, Science 227, 849 (1985).CrossRefPubMedGoogle Scholar
  48. [9-48]
    J. D. Dunitz, in Host-Guest Molecular Interactions: From Chemistry to Biology (D. J. Chadwick and K. Widdows, eds.), p. 92, John Wiley & Sons, Chichester, England (1991).Google Scholar
  49. [9-49]
    K. Mirsky, ACH-Models in Chemistry 130, 197 (1993); A. Gavezzotti and G. Filippini, ACH-Models in Chemistry 130, 205 (1993).Google Scholar
  50. [9-50]
    L. E. Depero, in Advances in Molecular Structure Research, Vol. 1 (M. Hargittaiandl. Hargittai, eds.), JAI Press, Greenwich, Connecticut (1995).Google Scholar
  51. [9-51]
    J. Maddox, Nature (London) 335, 201 (1988).CrossRefGoogle Scholar
  52. [9-52]
    C. P. Brock, Collected Abstracts, XVI Congress and General Assembly, International Union of Crystallography, Beijing, 1993, Paper MS-06.0.1 (p. 4).Google Scholar
  53. [9-53]
    D. Braga and F. Grepioni, Organometallics 10, 1254 (1991).CrossRefGoogle Scholar
  54. [9-54]
    A. L. Mackay, A Dictionary of Scientific Quotations, Adam Hilger, Bristol, England (1992).Google Scholar
  55. [9-55]
    P. M. Zorky and V. A. Koptsik, in Sovremennie Problemi Fizicheskoi Khimii (Ya. I. Gerasimov and P. A. Akishin, eds), Izdatel’stvo Moskovskogo Universiteta, Moscow (1979).Google Scholar
  56. [9-56]
    P. M. Zorky and E. E. Dashevskaya, ACH-Models in Chemistry 130, 247 (1993).Google Scholar
  57. [9-57]
    G. P. Charbonneau and Y. Delugeard, Acta Crystallogr., Sect. B 33, 1586 (1977); H. Cailleau, J. L. Bauduor, and C. M. E. Zeyen, Acta Crystallogr, Sect. B 35, 426 (1979); H. Takeuchi, S. Suzuki, A. J. Dianoux, and G. Allen, Chem. Phys. 55, 153 (1981).CrossRefGoogle Scholar
  58. [9-58]
    A. Almenningen, O. Bastiansen, L. Fernholt, B. N. Cyvin, S. J. Cyvin, and S. Samdal, J. Mol. Struct. 128, 59 (1985).CrossRefGoogle Scholar
  59. [9-59]
    T. R Martin, Phys. Rev. 95, 167 (1983).Google Scholar
  60. [9-60]
    M. Hargittai, Kern. Közlem. 50, 371 (1978).Google Scholar
  61. [9-61]
    U. Müller, Inorganic Structural Chemistry, John Wiley & Sons, Chichester, England (1993).Google Scholar
  62. [9-62]
    M. Hargittai and G. Jancsó, Z. Naturforsch., A 48, 1000 (1993).Google Scholar
  63. [9-63]
    G. Schultz and I. Hargittai, Acta Chim. Hung. 75, 381 (1973).Google Scholar
  64. [9-64]
    M. Hayashi, Y. Shiro, T. Oshima, and H. Murata, Bull. Chem. Soc. Jpn. 38, 1734 (1975).CrossRefGoogle Scholar
  65. [9-65]
    A. Domenicano and I. Hargittai (eds.), Accurate Molecular Structures. Their Determination and Importance, Oxford University Press, Oxford (1992).Google Scholar
  66. [9-66]
    I. Hargittai and M. Hargittai, in Molecular Structure and Energetics, Vol. 2 (J. F. Liebman and A. Greenberg, eds.), Chapter 1, VCH Publishers, Deerfield Beach, Florida (1986).Google Scholar
  67. [9-67]
    M. Hargittai and I. Hargittai, Phys. Chem. Miner. 14, 413 (1987).CrossRefGoogle Scholar
  68. [9-68]
    A. Domenicano and I. Hargittai, ACH-Models in Chemistry 130, 347 (1993).Google Scholar
  69. [9-69]
    M. Hargittai and I. Hargittai, J. Mol. Struct. 39, 79 (1977).CrossRefGoogle Scholar
  70. [9-70]
    W. A. Burns and K. R. Leopold, J. Am. Chem. Soc. 115, 11622 (1993).CrossRefGoogle Scholar
  71. [9-71]
    G. Forgács, M. Kolonits, and I. Hargittai, Struct. Chem. 1, 245 (1990).CrossRefGoogle Scholar
  72. [9-72]
    P. Scharfenberg and I. Hargittai, J. Mol. Struct. 112, 65 (1984).CrossRefGoogle Scholar
  73. [9-73]
    A. L. Mackay, Phys. Bull. 1976, 495.Google Scholar
  74. [9-74]
    A. L. Mackay, Kristallografiya 26, 910 (1981).Google Scholar
  75. [9-75]
    I. Hargittai and W. J. Orville Thomas (eds.). Diffraction Studies on Non-Crystalline Substances, Elsevier, Amsterdam (1981).Google Scholar
  76. [9-76]
    J. D. Bernai, Acta Phys. Acad. Sci. Hung. 8, 269 (1958).CrossRefGoogle Scholar
  77. [9-77]
    J. D. Bernai and C. H. Carlisle, Kristallografiya 13, 927 (1969).Google Scholar
  78. [9-78]
    N. V. Belov, Kristallografiya 17, 208 (1972).Google Scholar
  79. [9-79]
    A. Wickham, Selected Poems, Chatto and Windus, London (1971).Google Scholar
  80. [9-80]
    W. H. Zachariasen, J. Am. Chem. Soc. 54, 3841 (1932).CrossRefGoogle Scholar
  81. [9-81]
    A. R. Cooper, J. Non-Cryst. Solids 49, 1 (1982).CrossRefGoogle Scholar
  82. [9-82]
    A. Guinier, in Diffraction Studies on Non-Crystalline Substances (I. Hargittai and W. J. Orville Thomas, eds.), p. 411, Elsevier, Amsterdam (1981).Google Scholar
  83. [9-83]
    D. Levine and P. J. Steinhardt, Phys. Rev. Lett. 53, 2477 (1984).Google Scholar
  84. [9-84]
    M. La Brecque, Mosaic 18, 1 (1987/88).Google Scholar
  85. [9-85]
    R. Penrose, Eureka No. 39; Math. Intell. 2, 32 (1979/80). [Reprinted also in Per. Mineral. 59, 69 (1990).]CrossRefGoogle Scholar
  86. [9-86]
    B. Grünbaum and G. C. Shephard, Tilings and Patterns, W. H. Freeman & Co., New York (1987).Google Scholar
  87. [9-87]
    M. Gardner, Sci. Am. 236, 110 (1977).CrossRefGoogle Scholar
  88. [9-88]
    A. L. Mackay, Physica A 114, 609 (1982).CrossRefGoogle Scholar
  89. [9-89]
    A. L. Mackay, Two Lectures on Fivefold Symmetry at the Hungarian Academy of Sciences, Budapest, September, 1982.Google Scholar
  90. [9-90]
    I. Hargittai, Per. Mineral. 61, 9 (1992).Google Scholar
  91. [9-91]
    D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, Phys. Rev. Lett. 53, 1951 (1984).CrossRefGoogle Scholar
  92. [9-92]
    A. L. Mackay, Int. J. Rapid Solidification 2, SI (1987).Google Scholar
  93. [9-93]
    M. Ronchetti, Per. Mineral. 59, 219 (1990).Google Scholar
  94. [9-94]
    L. Loreto and M. Ronchetti (eds.), Topics on Contemporary Crystallography and Quasicrystals, Per. Mineral. 59, 1–3, Special Issue (1991).Google Scholar
  95. [9-95]
    I. Hargittai (ed.), Quasicrystals, Networks, and Molecules of Fivefold Symmetry1, VCH, New York (1990).Google Scholar
  96. [9-96]
    M. V. Jaric (ed.), Aperiodicity and Order, Vol. 1, Introduction to Quasicrystals, Academic Press, San Diego (1988).Google Scholar
  97. [9-97]
    M. V. Jaric (ed.), Aperiodicity and Order, Vol. 2, Introduction to the Mathematics of Quasicrystals, Academic Press, San Diego (1989).Google Scholar
  98. [9-98]
    M. V. Jaric and A. Gratias (eds.), Aperiodicity and Order, Vol. 3, Extended Icosahedral Structures, Academic Press, San Diego (1989).Google Scholar
  99. [9-99]
    A. Csanády, K. Papp, M. Dobosy, and M. Bauer, Symmetry 1, 75 (1990).Google Scholar
  100. [9-100]
    I. Hargittai (ed.), Fivefold Symmetry, World Scientific, Singapore (1992), p. xiv.Google Scholar
  101. [9-101]
    F Dénoyer, in Quasicrystals, Networks, and Molecules of Fivefold Symmetry (I. Hargittai, ed.), VCH, New York (1990).Google Scholar
  102. [9-102]
    I. Hargittai, Math. Intell. 14, 58 (1992).Google Scholar
  103. [9-103]
    R J. Steinhardt, Endeavour, New Ser. 14(3), 112 (1990).CrossRefGoogle Scholar
  104. [9-104]
    N. D. Mermin, Phys. Rev. Lett. 68, 1172 (1992).PubMedCrossRefGoogle Scholar
  105. [9-105]
    A. L. Mackay, J. Non-Cryst. Solids 97 & 98, 55 (1987).CrossRefGoogle Scholar
  106. [9-106]
    C. Bunn, Crystals: Their Role in Nature and Science, Academic Press, New York (1964).Google Scholar

Copyright information

© Plenum Press 1995

Personalised recommendations