Abstract
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.KeywordsMetallic GlassFlat SpaceMatching RuleStandard OrientationIcosahedral ClusterThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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