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These non-periodic structures are resolved by establishing whether a structure will accommodate or reject additional local structures. This property, structural selectivity, is treated as a signature of an underlying ordering principle. The major result of this paper is the determination that roughly 35% of the non-periodic structures are selective and, hence, ordered in some way. This selectivity extends up to a diversity of \u223c9, well beyond the upper threshold for diversity in periodically ordered states.<\/jats:p>","DOI":"10.1063\/5.0330869","type":"journal-article","created":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T11:34:12Z","timestamp":1781004852000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["What lies between crystal and randomly packed structures? 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