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Volume 35, Number 4, pages 441-457 (2024)
https://doi.org/10.26830/symmetry_2024_4_441
INTERRELATION OF PENTAGON TILINGS AND OPEN PACKINGS OF EDGE-SHARING ICOSAHEDRA
Robert Earl Dewar
Independent Artist, Tehachapi, California. U.S.A.
Email: robertearldewar1@gmail.com
Abstract: A new method for relating pentagon tilings to open packings of edge-sharing icosahedra is presented. It assumes that the geometric structure of an open packing of icosahedra is in a geometric relationship with one or more tilings of regular pentagons. By following a simple procedure for placing icosahedra into the plane of a pentagon tiling, one can build up layers of an open packing of edge-sharing icosahedra. Once an open packing structure has been determined, its level of complexity can be increased by substituting the icosahedra with other geometric structures that have analogous symmetry. This inevitably leads to the introduction of new dissymmetric elements.
Keywords: Pentagon, icosahedron, dodecahedron, pentagonal antiprism, dissymmetry.
References:
Darvas, G. (1998) Ontological Levels and Symmetry Breaking, The Paideia Archieve: Twentieth World Congress of Philosophy, 37,1,34-43. https:///doi.org/10.5840/wcp20-paidea199837648
Dewar, R. E. (2021) On the Complexity of Polyhedron Aggregate Structures, Symmetry: Culture and Science, 32, 1, 59-81. https://doi.org/10.26830/symmetry_2021_1_059-081.
Pearce, P. (1978) Structure in Nature Is a Strategy for Design, Cambridge, MA: The MIT Press, xviii+245pp.
Kepler, J. (1997) The Harmony of the World, United Kingdom: American Philosophical Society, xli+549pp.
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