Search results

[[File:AmmannA1Prototiles.svg|thumb|The prototiles for A1 tilings, with decorations.]] ...=Branko | last2=Shephard | first2=Geoffrey C. |name-list-style=amp | title=Tilings and Patterns | location=New York | publisher=W. H. Freeman | year=1986 | is ...

...ubstitution tiling]]. It is, apart from the [[Penrose tiling|Penrose rhomb tilings]] and their variations, a classical candidate to model 5-fold (respectively ...The Penrose rhomb tilings are locally derivable from the Tübingen triangle tilings. ...

...f> some of them [[mirror image]]s, and repeating this process leads to a [[aperiodic tiling|non-periodic tiling]] of the plane. The sphinx is therefore a [[rep- ==General tilings== ...

[[File:AmmanBeenker.png|thumb|A portion of tiling by Ammann's aperiodic A5 set of tiles, decorated with finite, local matching rules which force in ...a nonperiodic [[tessellation|tiling]] which can be generated either by an aperiodic set of [[prototile]]s as done by [[Robert Ammann]] in the 1970s, or by the ...

...ic tiling]]s, though strictly speaking it is the tiles themselves that are aperiodic. (The tiling itself is said to be "nonperiodic".) ...bbreviations used in the second table. The second table contains all known aperiodic sets of tiles and gives some additional basic information about each set. T ...

...group]] but not a two-dimensional family of symmetries. There exist binary tilings with tiles of arbitrarily small area. ...|Károly Böröczky|hu|Böröczky Károly (matematikus, 1964)}}. Closely related tilings have been used since the late 1930s in the [[Smith chart]] for radio engine ...

...both [[reflection symmetry]] and fivefold [[rotational symmetry]]. Penrose tilings are named after mathematician and physicist [[Roger Penrose]], who investig ...ed in this manner, each variation yields infinitely many different Penrose tilings. ...

...tiling#Cut-and-project method|cut-and-project method]] for constructing [[aperiodic tiling]]s. Therefore, the vertices of the [[pinwheel tiling]] and [[Penrose ...

Two different [[aperiodic tiling]]s with 5-fold symmetry can be obtained by projecting two-dimensiona ...loid Tetracombs'', Manuscript (2006) ''(Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)'' Model 1 ...

| title=Aperiodic tilings, positive scalar curvature and amenability of spaces ...

...een used in other fields including mathematics and physics. For example, [[aperiodic tiling]]s such as [[Penrose tiling]]s can be modeled using Zometool. The le ...

...ose|author-link=Roger Penrose| title=Pentaplexity: a class of non-periodic tilings of the plane|journal= [[Eureka (University of Cambridge magazine)|Eureka]]| ...=171–188|doi=10.3390/sym6020171|title=Development of Symmetry Concepts for Aperiodic Crystals|first=Ted|last= Janssen|issue= 2|author-link=Ted Janssen|doi-acces ...