Tilings

Some articles on tilings, tiling:

Ammann–Beenker Tiling - Description of The Tiles
... The most common choice of tileset to produce the Ammann–Beenker tilings includes a rhombus with 45- and 135-degree angles (these rhombi are shown in blue in the diagram at ... show the pieces and a portion of the tilings ... Katz has studied the additional tilings allowed by dropping the vertex constraints and imposing only the requirement that the edge arrows match ...
The Pinwheel Tilings
... construction of Conway to define Pinwheel tilings ... Formally, the Pinwheel tilings are the tilings whose tiles are isometric copies of, with a tile maying intersect another tile only either on a whole side or on half the length side, and such that the ... Given any Pinwheel tiling, there is a Pinwheel tiling which, once each tile is divided in five following the Conway construction and the result is dilated by a factor, is ...
Ammann–Beenker Tiling
... In geometry, an Ammann–Beenker tiling is a nonperiodic tiling which can be generated either by an aperiodic set of prototiles as done by Robert Ammann in the 1970s, or by the cut-and-project method as done ... Because all tilings obtained with the tiles are non-periodic, Ammann–Beenker tilings are considered aperiodic tilings ... They are one of the five sets of tilings discovered by Ammann and described in Tilings and Patterns ...
Substitution Tiling
... substitution is a useful method for constructing highly ordered tilings ... importantly, some tile substitutions generate aperiodic tilings, which are tilings whose prototiles do not admit any tiling with translational symmetry ... The most famous of these are the Penrose tilings ...
Truncated Heptagonal Tiling - Related Polyhedra and Tilings
... This hyperbolic tiling is topologically related as a part of sequence of uniform truncated polyhedra with vertex configurations (3.2n.2n), and Coxeter group symmetry ... Dimensional family of truncated polyhedra and tilings 3.2n.2n Symmetry *n32 Spherical Euclidean Hyperbolic.. ... a Wythoff construction there are eight hyperbolic uniform tilings that can be based from the regular heptagonal tiling ...