Model of Icosahedral Order
Metallic glasses, quasicrystals, and crystals may share identical local icosahedral order. This type of ordering extends to fill a three-dimensional curved space, producing an icosahedral “polytope” with perfect short and long-range icosahedral order. In this paper I demonstrate how to flatten the polytope and fill space with structures possessing the short-range order of the polytope but various types of long-range order. Both the rhombohedral packing units required to construct a three-dimensional Penrose pattern and long-range orientational order arise from rolling the polytope along special paths in three-dimensional flat space.
KeywordsZinc Magnesium Prolate
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