Abstract
Aperiodic tilings are non-periodic tilings defined by local rules. They are widely used to model quasicrystals, and a central question is to understand which of the non-periodic tilings are actually aperiodic. Among tilings, those by rhombi can be easily seen as approximations of surfaces in higher dimensional spaces. In particular, those which approximate irrational planes are non-periodic. But which ones are also aperiodic? This paper introduces the notion of subperiod, which links algebraic properties of a plane with geometric properties of the tilings that approximate it. A necessary and sufficient condition is obtained for tilings that can be seen in the four dimensional Euclidean space. This result is then applied to some examples in higher codimensions, notably tilings with n-fold rotational symmetry.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
