{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:01:30Z","timestamp":1760241690424,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2018,7,12]],"date-time":"2018-07-12T00:00:00Z","timestamp":1531353600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["JP16H01728, JP16K00024 and JP17K14580"],"award-info":[{"award-number":["JP16H01728, JP16K00024 and JP17K14580"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The present paper introduces a method for designing 3D objects that are initially incomplete, but become complete when they are augmented by their mirror reflections. Physically, the mirror image is plane-symmetric with respect to the original object, but the perceived shape is not necessarily symmetric because of optical illusion. In the proposed method, a 2D shape that is not necessarily symmetric is divided into two halves, one of which is used to construct a solid object. When we place the solid object on a plane mirror, the other half is generated by the mirror, and thus, a whole shape is realized. In the present study, the design algorithm and examples are shown, and the condition for constructability is also presented.<\/jats:p>","DOI":"10.3390\/sym10070275","type":"journal-article","created":{"date-parts":[[2018,7,12]],"date-time":"2018-07-12T11:19:24Z","timestamp":1531394364000},"page":"275","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Reflexively-Fused Cylinders"],"prefix":"10.3390","volume":"10","author":[{"given":"Kokichi","family":"Sugihara","sequence":"first","affiliation":[{"name":"Meiji Institute for Advanced Study of Mathematical Sciences, Tokyo 164-8525, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Masaki","family":"Moriguchi","sequence":"additional","affiliation":[{"name":"Meiji Institute for Advanced Study of Mathematical Sciences, Tokyo 164-8525, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,7,12]]},"reference":[{"key":"ref_1","unstructured":"The Bunkamura Museum of Art (2014). 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Manuf."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1007\/s13160-016-0233-9","article-title":"A new type of impossible objects that become partly invisible in a mirror","volume":"33","author":"Sugihara","year":"2016","journal-title":"Jpn. J. Ind. Appl. Math."},{"key":"ref_7","first-page":"1","article-title":"Topology-disturbing objects: A new class of 3D optical illusion","volume":"12","author":"Sugihara","year":"2017","journal-title":"J. Math. Arts"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.jmp.2015.07.001","article-title":"Height reversal generated by rotation around a vertical axis","volume":"68\u201369","author":"Sugihara","year":"2015","journal-title":"J. Math. Psychol."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Sugihara, K. (2016). Anomalous mirror symmetry generated by optical illusion. Symmetry, 8.","DOI":"10.3390\/sym8040021"},{"key":"ref_10","unstructured":"Suzuki, R., Moriguchi, M., and Imai, K. (2017, January 16\u201319). Generation and optimization of multi-view wire art. Proceedings of the 25th Pacific Conference on Computer Graphics and Applications (Pacific Graphics 2017) Posters, Taipei, Taiwan."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"293","DOI":"10.3758\/BF03205849","article-title":"Visual discrimination between rectangular and nonrectangular parallelopipeds","volume":"12","author":"Perkins","year":"1972","journal-title":"Percept. Psychophys."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/7\/275\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:11:49Z","timestamp":1760195509000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/7\/275"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,12]]},"references-count":11,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2018,7]]}},"alternative-id":["sym10070275"],"URL":"https:\/\/doi.org\/10.3390\/sym10070275","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2018,7,12]]}}}