On tilings and patterns on hyperbolic surfaces and their relation to structural chemistry

ChemPhysChem

Volumn 2, Issue 7, 2001, Pages 413-422

  Nesper, Reinhard ^a   Leoni, Stefano ^b  

^a ETH ZURICH   (Switzerland)

^b MAX PLANCK INSTITUTE FOR CHEMICAL PHYSICS OF SOLIDS   (Germany)

Author keywords

Crystallography; Hyperbolic frameworks; Hyperbolic tilings; Periodic nodal surfaces; Solids

Indexed keywords

CRYSTALLOGRAPHY; SOLIDS; TEXTURES; TOPOLOGY;

CONSTRUCTION PRINCIPLE; HYPERBOLIC FRAMEWORKS; HYPERBOLIC TILINGS; NODAL SURFACE; STRUCTURAL CHEMISTRY; SURFACE MODULATIONS; TEXTURE INFORMATION; THREE-DIMENSIONAL FRAMEWORKS;

FOURIER SERIES;

EID: 0000026732     PISSN: 14394235     EISSN: None     Source Type: Journal    
DOI: 10.1002/1439-7641(20010716)2:7<413::AID-CPHC413>3.0.CO;2-V     Document Type: Article

References (31)

1. I. Stewart, Sci. Am. 1999, 281(1), 96-98.
2. E. S. Fedorov, Zap. Mineral. Obch. 1891, 23, 2, 345-390.
3. R. Penrose, Math. Intell. 1979, 2, 32.
4. D. Stechtman, I. Blech, D. Gratias, J. W. Cahn, Phys. Rev. Lett. 1984, 53, 1951.
5. A. L. Mackay, Physica A 1982, 114, 609.
6. O. D. Friedrichs, A. W. Dress, D. H. Huson, J. Klinowski, A. L. Mackay, Nature 1999, 400, 644-647.
7. L. Faelth, S. Andersson, Z. Kristallogr. 1982, 160, 313.
8. H.G. von Schnering, R. Nesper, Angew. Chem. 1987, 99, 1097-1119;
9. Angew. Chem. Int. Ed. Engl. 1987, 26, 1059-1080.
10. H.G. von Schnering, R. Nesper, Z. Phys. B 1991, 83, 407-412.
11. S. Andersson, S. Hyde, H. G. von Schnering, Z. Kristallogr. 1984, 168, 1-17.
12. S. Hyde, S. Andersson, K. Larsson, Z. Blum, T. Landh, S. Lidin, B. W. Ninham, The Language of Shape: The Role of Curvature in Condensed Matter: Physics, Chemistry, and Biology, Elsevier, Amsterdam, 1997.
13. S. Andersson, M. Jacob, The Nature of Mathematics and The Mathematics of Nature, Elsevier, Amsterdam, 1998.
14. S. Leoni, Ph.D. thesis, ETH Zürich (Switzerland), 1998.
15. U. S. Schwarz, G. Gompper, Phys. Rev. E 1999, 59, 5528-55.
16. S. Leoni, R. Nesper, Acta Crystallogr. A 2000, 56, 383-393.
17. S. T. Hyde, S. Andersson, Z. Kristallogr. 1984, 168, 221-254.
18. W. Fischer, E. Koch, International Tables for Crystallography, Vol. A (Ed.: T. Hahn), Kluwer Academic, Dordrecht, 1989, chap. 14.
19. E. Koch, W. Fischer, International Tables for Crystallography, Vol. A (Ed.: T. Hahn), Kluwer Academic, Dordrecht, 1989, chap. 15.
20. U. Shmueli, International Tables for Crystallography, Vol. A (Ed.: U. Shmueli), Kluwer Academic, Dordrecht, 1993, chap. 1.4.
21. H. G. von Schnering, unpublished results.
22. E. Hellner, E. Koch, A. Reinhardt, Physik Daten - Physics Data 1981, Fachinformationszentrum Karlsruhe, 16-2, 1-67.
23. J. C. C. Nitsche, Arch. Ration. Mech. Anal. 1985, 89, 1-19.
24. S. T. Hyde in Defects and Processes in the Solid State: Geoscience Applications (Eds.: J. N. Boland, J. D. Fitz Gerald), Elsevier, Amsterdam, 1993.
25. S. T. Hyde, C. Oguey, Eur. Phys. J. B 2000, 16, 613-630.
26. S. T. Hyde, S. Ramsden in Mathematical Chemistry, Vol. 6 (Eds.: D. Bonchev, D. Rouvray), Gordon and Breach, New York, NY, 2000, chap. 2.
27. H. Terrones, A. L. Mackay, Prog. Cryst. Growth Charact. Mater. 1997, 34, 25-36.
28. S. Leoni, S. P. Piotto, R. Nesper, unpublished results.
29. P. Engel, T. Matsumoto, G. Steinmann, H. Wondratschek, The Noncharacteristic Orbits of the Space Groups, Oldenbourg, Munich, 1994.
30. M. O'Keeffe, G. B. Adams, O. F. Sankey, Phys. Rev. Lett. 1992, 68, 2325.
31. A. Fogden, S. T. Hyde, Eur. Phys. J. B 1999, 7, 91-104.