{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T11:35:02Z","timestamp":1760441702727,"version":"build-2065373602"},"reference-count":7,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,12,9]],"date-time":"2021-12-09T00:00:00Z","timestamp":1639008000000},"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>Euclidean tilings are constantly applied to many fields of engineering (mechanical, civil, chemical, etc.). These tessellations are usually named after Cundy &amp; Rollett\u2019s notation. However, this notation has two main problems related to ambiguous conformation and uniqueness. This communication explains the GomJau-Hogg\u2019s notation for generating all the regular, semi-regular (uniform) and demi-regular (k-uniform, up to at least k = 3) in a consistent, unique and unequivocal manner. Moreover, it presents Antwerp v3.0, a free online application, which is publicly shared to prove that all the basic tilings can be obtained directly from the GomJau-Hogg\u2019s notation.<\/jats:p>","DOI":"10.3390\/sym13122376","type":"journal-article","created":{"date-parts":[[2021,12,10]],"date-time":"2021-12-10T02:07:18Z","timestamp":1639102038000},"page":"2376","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["GomJau-Hogg\u2019s Notation for Automatic Generation of k-Uniform Tessellations with ANTWERP v3.0"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7810-9589","authenticated-orcid":false,"given":"Valentin","family":"Gomez-Jauregui","sequence":"first","affiliation":[{"name":"Department of Geographic Engineering and Graphical Expression Techniques, Universidad de Cantabria, 39005 Santander, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Harrison","family":"Hogg","sequence":"additional","affiliation":[{"name":"Spotify, London WC2N 6AT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cristina","family":"Manchado","sequence":"additional","affiliation":[{"name":"Department of Geographic Engineering and Graphical Expression Techniques, Universidad de Cantabria, 39005 Santander, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cesar","family":"Otero","sequence":"additional","affiliation":[{"name":"Department of Geographic Engineering and Graphical Expression Techniques, Universidad de Cantabria, 39005 Santander, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,9]]},"reference":[{"key":"ref_1","unstructured":"Otero, C. (1990). Dise\u00f1o Geom\u00e9trico de C\u00fapulas No Esf\u00e9ricas Aproximadas por Mallas Triangulares con un N\u00famero M\u00ednimo de Longitudes de Barra. [Ph.D. Thesis, University of Cantabria]."},{"key":"ref_2","unstructured":"Cundy, H.M., and Rollett, A.P. (1981). Mathematical Models, Tarquin Publications."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1061\/(ASCE)ST.1943-541X.0000532","article-title":"Generation and Nomenclature of Tessellations and Double-Layer Grids","volume":"138","author":"Otero","year":"2012","journal-title":"J. Struct. Eng."},{"key":"ref_4","unstructured":"Gr\u00fcnbaum, B., and Shephard, G.C. (1986). Tilings and Patterns, W. H. Freeman & Co."},{"key":"ref_5","unstructured":"Hogg, H., and Gomez-Jauregui, V. (2021, October 17). Antwerp v3.0.0. Available online: https:\/\/antwerp.hogg.io."},{"key":"ref_6","unstructured":"Galebach, B.L. (2021, November 30). Number of N-Uniform Tilings. Available online: https:\/\/www.probabilitysports.com\/tilings.html."},{"key":"ref_7","unstructured":"Khan, A.A., Laghari, A.A., and Awan, S.A. (2021). Machine Learning in Computer Vision: A Review. EAI Endorsed Trans. Scalable Inf. Syst., 8."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/12\/2376\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:43:52Z","timestamp":1760168632000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/12\/2376"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,9]]},"references-count":7,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["sym13122376"],"URL":"https:\/\/doi.org\/10.3390\/sym13122376","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,12,9]]}}}