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Volume 32, Number 2, pages 129-132 (2021)
https://doi.org/10.26830/symmetry_2021_2_129
PENTILES: DISCOVERY AND CONCEPTS
Haresh Lalvani1,2
1 Center for Experimental Structures, School of Architecture, Pratt Institute, New York, NY 11205, U.S.A.
E-mail: hlalvani@pratt.edu
2 Lalvani Studio, 164 Bank Street, #2B, New York, NY 10014, U.S.A.
E-mail: hlalvani@gmail.com
Abstract: Pentiles is a 2D kit of even-sided tile shapes projected from 5D. All tiles have equal edges and their directions are parallel to the 5 lines that join the center of a regular pentagon to its vertices. The centrally symmetric 2D projection of a 5D cube provides a master diagram of all tiles shapes, convex and concave, within this set. Pentiles is the n=5 case and is part of an infinite set of kits from other values of n. The angles of the tiles are described in terms of angle-numbers as integer multiples of the central angle of a regular 2n-gon. Pentiles are part of a larger body of author’s work on higher dimensions.
Keywords: tiles, building systems, non-periodic tiling, higher dimensions.
References:
Coxeter, H.S.M. (1973) Regular Polytopes. Dover, 321 pp.
Lalvani, H. (1981) Multi-dimensional Periodic Arrangements of Transforming Space Structures. PhD Dissertation, University of Pennsylvania, Ann Arbor: University Microfilms.
Lalvani, H. (1982) Structures on Hyper-Structures. New York: H. Lalvani, 112 pp.
Lalvani, H. (1986-1987/2011) Non-periodic space structures. International Journal of Space Structures, 2, 93-108. https://doi.org/10.1177/026635118700200204; republ. in: vol. 26, 3, 139-154, 2011, as part of the Special Issue ‘Celebrating 25 Years Devoted to Space Structures’. https://doi.org/10.1260/0266-3511.26.3.139
Lalvani, H. (1986) Crescent-shaped Polygonal Tiles. U.S. Patent 4,620,998, November 4. https://www.google.com/patents/US4620998
Lalvani, H. (1991) Non-periodic and Periodic Layered Space Frames Having Prismatic Nodes. U.S. Patent 5,007,220, April 16. https://www.google.ch/patents/US5007220
Lalvani, H. (1996) Periodic and Non-Periodic Tilings and Blocks from Prismatic Nodes. U.S. Patent 5,575,125, November 19.
Lalvani, H. (1998) Periodic and Non-Periodic Non-convex and Convex Tilings and Blocks from Prismatic Nodes, U.S. Patent 5,775,040, July 7. https://www.google.com/patents/US5775040
Lalvani, H. (2018) Morphological Universe: Genetics and epigenetics in form-making. Symmetry: Culture and Science, 29, 1, 7-240. https://doi.org/10.26830/symmetry_2018_1_007
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