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Symmetry: Culture and Science
Volume 35, Number 3, pages 311-314 (2024)
https://doi.org/10.26830/symmetry_2024_3_311

NEW METHOD RELATES PENTAGON TILE PATTERNS TO OPEN PACKINGS OF ICOSAHEDRA

Robert Earl Dewar

Independent Artist, Tehachapi, California. U.S.A.
Email: robertearldewar1@gmail.com

Abstract: It is not possible to tile the plane with regular pentagons without gaps. If the gap areas are defined as black voids, then a binary coloring scheme can be used to differentiate the pentagon tiles into two groups. I have devised a new method using this scheme to describe any pentagon tiling of regular pentagons as a cross section of an open packing of icosahedra. I will demonstrate how to use this method to construct an open packing of icosahedra from a pentagon-rhombus tiling. After that, I will demonstrate how to expand it into an aggregate of dodecahedra interspaced with pentagonal antiprisms.

Keywords: Intercultural Communication, Power Distance, Symmetry/Asymmetry

References:
Grünbaum, B., Shephard, G., (1987) Tilings and Patterns. New York, NY: W. H. Freeman, 699 pp.

Pearce, P., (1978) Structure in Nature Is a Strategy for Design. Cambridge, MA: The MIT Press, 245 pp.

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