{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,20]],"date-time":"2025-12-20T22:30:46Z","timestamp":1766269846518,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2016,4,8]],"date-time":"2016-04-08T00:00:00Z","timestamp":1460073600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper introduces a new concept of mirror symmetry, called \u201canomalous mirror symmetry\u201d, which is physically impossible but can be perceived by human vision systems because of optical illusion. This symmetry is characterized geometrically and a method for creating cylindrical surfaces that create this symmetry is constructed. Examples of solid objects constructed by a 3D printer are also shown.<\/jats:p>","DOI":"10.3390\/sym8040021","type":"journal-article","created":{"date-parts":[[2016,4,8]],"date-time":"2016-04-08T21:02:38Z","timestamp":1460149358000},"page":"21","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Anomalous Mirror Symmetry Generated by Optical Illusion"],"prefix":"10.3390","volume":"8","author":[{"given":"Kokichi","family":"Sugihara","sequence":"first","affiliation":[{"name":"Meiji Institute for the Advanced Study of Mathematical Sciences, Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo 164-8525, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,4,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1633","DOI":"10.3390\/sym7031633","article-title":"Mirror symmetry and polar duality of polytopes","volume":"7","author":"Cox","year":"2015","journal-title":"Symmetry"},{"key":"ref_2","unstructured":"Hori, K., Katz, S., Klemm, A., Pandharipande, R., Thomas, R., Vafa, C., Vakil, R., and Zaslow, E. (2003). Mirror Symmetry, American Mathematical Society."},{"key":"ref_3","unstructured":"Gregory, R.L. (1970). The Intellignet Eye, Weidenfeld and Nicolson."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"54","DOI":"10.3390\/sym3010054","article-title":"The influence of perception on the distribution of multiple symmetries in nature and art","volume":"3","year":"2011","journal-title":"Symmetry"},{"key":"ref_5","unstructured":"Sugihara, K. (2015, January 5\u20139). Design of ambiguous cylinders. Proceedings of the Asian Forum on Graphic Science, Bangkok, Tailand."},{"key":"ref_6","unstructured":"Sugihara, K. (2015). Joy of Anomalous Solids: How to Make Anomalous Objects That Change Their Appearances in a Mirror, Sugi Lab., Inc."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1007\/978-3-540-24672-5_42","article-title":"Reconstruction of 3-D deformed symmetric curves from perspective images without discrete features","volume":"3023","author":"Hong","year":"2004","journal-title":"Lecture Notes Comput. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"365","DOI":"10.3390\/sym3020365","article-title":"Any pair of 2D curves is consistent with a 3D symmetric interpretation","volume":"3","author":"Sawada","year":"2011","journal-title":"Symmetry"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1588","DOI":"10.1109\/JPROC.2014.2344001","article-title":"Detecting 3-D mirror symmetry in a 2-D camera image for 3-D shape recovery","volume":"102","author":"Sawada","year":"2014","journal-title":"Proc. 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Psychophys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1068\/p050393","article-title":"How good a bet is good form?","volume":"5","author":"Perkins","year":"1976","journal-title":"Perception"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/8\/4\/21\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:21:55Z","timestamp":1760210515000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/8\/4\/21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,4,8]]},"references-count":14,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2016,4]]}},"alternative-id":["sym8040021"],"URL":"https:\/\/doi.org\/10.3390\/sym8040021","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2016,4,8]]}}}