Non-periodic space structures

International Journal of Space Structures

Volumn 26, Issue 3, 2011, Pages 139-154

  Lalvani, Haresh ^a,b  

^a PRATT INSTITUTE   (United States)

^b NEW YORK INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GEOMETRY; SPACE APPLICATIONS;

DIMENSIONAL GRIDS; HIGHER-DIMENSIONAL; MULTI-LAYERED; REGULAR POLYGON; SPACE FILLING; SPACE STRUCTURE; SYMMETRY GROUPS; THREE DIMENSIONAL SPACE;

SPACE PLATFORMS;

EID: 80052910934     PISSN: 09560599     EISSN: 20598033     Source Type: Journal    
DOI: 10.1260/0266-3511.26.3.139     Document Type: Article

References (39)

1. GARDNER, M., Scientific American (Jan., 1977). 110-121.
2. DE BRUIJN, N., Algebraic theory of Penrose's non-periodic tilings of the plane: 1, Proc. Koninklijke Nederlandse Akademie van Wetenschappen, A84(1) (1981), 39-66.
3. LALVANI, H., unpublished work. 1981.
4. M. Gubeli's 'Pentalbi' toy uses this crescent; author's work is independent (unpublished, 1982).
5. MARTIN, G. E., Transformation Geometry, Springer-Verlag, New York. 1982, p. 128.
6. LALVANI, H., unpublished work, 1983; displayed at Gallery 91, NY, Feb. 1985;
7. see also Industrial Design (July Aug., 1985), 129.
8. Displayed at Gallery 91, NY. April, 1986.
9. LALVANI. H., Multi-dimensional periodic arrangements of transforming space structures, PhD Thesis, University of Pennsylvania, 1981, pp. 12 19, 207, 217, 219.
10. LALVANI, H., Structures on Hyper-siructures, Lalvani, New York, 1982, pp. 8-10, 63, 107 8 (ill. 1-3).
11. LALVANI, H., Generative morphology of curved space structures. In: Proc. Int. Symp. Architectural Fabric Structures, Vol. 1, Architectural Fabric Structures Institute, Glenview, Chicago, 1984, pp. 142 50.
12. LALVANI, H., Abstracts, Bacteriophage Meetings, Cold Spring Harbor Laboratory, N.Y., 1976, cover; a non-periodic pentagonal tessellation based on Fig. 13 is also shown on the back cover.
13. CRITCHLOW, K., Order in Space, Viking, New York, 1970, p. 95; overlay of great circles of the three groups shown.
14. FULLER, R. B., Synergetics 2, Macmillan, New York, 1979. plate 32; overlay of all great circles of the cuboctahedron and icosahedron shown.
15. PELLETIER, M., personal communication; suggested a node from the overlapping great circles of the three groups.
16. FULLER. R. B., Synergetics 1, Macmillan, New York, 1975, pp. 34, 58.
17. LALVANI, H., Transpolyhedra, Lalvani, New York, 1977, pp. 4, 29-41, 59-68.
18. COXETER, H. S. M., Regular Polytopes, Dover, New York, 1973, p. 256.
19. COXETER, H. S. M. and BALL, R. W. W., Mathematical Recreations and Essays, Macmillan, New York, 1947, p. 142; 6-and 9-cells of the octahedral group, and 6-, 10-and 15-cells of the icosahedral group mentioned here.
20. MIYAZAKI, K., Polyhedra and Architecture (in Japanese), Shokokusha, Japan, 1979, p. 175; cells of n = 9 are illustrated.
21. First known to the author via Dr A. Tyng (1978) nd attributed to D. Stuart.
22. SCHULMANN, J. L., Les Rhomboédres: Geometric ('1 Morphogenesis, Ecole Speciale d'Architecture, Paris, l9O, pp. 86-9.
23. The n -10 and 15 cases were independently developed by P. Kramer er at and the author; systematic enumeration to appear in a joint publication (Ref. 23).
24. HAASE, R., KRAMER, L., KRAMER. P. and LALVANI, H., Polyhedra of three quasilattices associated with the icosahedral group, submitted for publication.
25. LEVINE, D., LEVINE, D. and STEINHARDT, P., Quasi-crystals I: Definition and Structure, Preprint, Department of Physics, University of Pennsylvania (Aug., 1985), 38.
26. MIYAZAKI, K. and TAKADA, I., Uniform ant-hills in the world of golden isozonohedra, Structural Topology, 4 (1980), 21.
27. MACKAY, A. L., Crystallography and the Penrose pattern, Physica, 114A (1982), 609-13.
28. KRAMER, P., On the theory of a non-periodic quasi-lattice associated with the icosahcdral group. Z. Naturj., 40a (1985), 775-88.
29. KRAMER, P. and NERI, R., On periodic and non-periodic space-fillings of obtained by projection, Acta Cryst., A40 (1984), 580-7.
30. LEVINE, D. and STEINHARDT, P., Quasicrystals: a new class of ordered structures, Phys. Rev. Lett., 53(26) (1984), 2477-80.
31. SHECTMAN, D., BLECH, I., GRATIAS, D. and CAHN, J. W., Metallic phase with long-range orientational order and no translational symmetry, Phys. Rev. Lett., 53(20) (1984), 1951-3.
32. MIYAZAKI, K., Tower of Bubbles (in Japanese), Shokokusha, Japan, 1985.
33. LALVANI, H., Non-periodic space-fillings with golden polyhedra. In: Proc. First Jut. Conf. Lightweight Structures in Architecture, Sydney, Australia. August, 1986.
34. The vertices of the projections are similar to the diffraction pattern of Shectman et al.28
35. OXETER, H. S. M., LONGUET-HIGGINS, M. S. and MILLER, J. C. P., Phil. Trans., 246A (1954), 401-50.
36. LALVANI, H., Generative morphology of transforming space structures. In: Proc. Third Int. Conf. Space Structures, ed. H. Nooshin, Elsevier Applied Science, London, 1984, p. 138.
37. PEARCE, P., Structure in Nature is a Strategy for Design, M.I.T., 1978, pp. 66, 148.
38. MACKAY, A. L., Crystal symmetry, Physics Bulletin (Nov., 1976), 495.
39. BAER, S., The Zome Primer, Zomeworks Corp., Albuquerque, New Mexico, 1970.