{"title":"An Effective Construction for Cut-And-Project Rhombus Tilings with Global n-Fold Rotational Symmetry","authors":"Victor H. Lutfalla","doi":"10.4230/OASIcs.AUTOMATA.2021.9","DOIUrl":"https://doi.org/10.4230/OASIcs.AUTOMATA.2021.9","url":null,"abstract":"We give an explicit and effective construction for rhombus cut-and-project tilings with global n-fold rotational symmetry for any n. This construction is based on the dualization of regular n-fold multigrids. The main point is to prove the regularity of these multigrids, for this we use a result on trigonometric diophantine equations. A SageMath program that computes these tilings and outputs svg files is publicly available in [7]. 2012 ACM Subject Classification Mathematics of computing → Discrete mathematics; Mathematics of computing → Combinatorics","PeriodicalId":124625,"journal":{"name":"International Workshop on Cellular Automata and Discrete Complex Systems","volume":" 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114053016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}