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...

1/\sigma .} The silver ratio appears prominently in the Ammann–Beenker tiling, a non-periodic tiling of the plane with octagonal symmetry, build from a square...

octagonal variant for the Ammann–Beenker tiling. Ammann's name became that of the perennial second. It is acknowledged however that Ammann first proposed the...

polygon, and the only tiling that can admit a regular octagon. The Ammann–Beenker tiling is a nonperiodic tesselation of prototiles that feature prominent...

Edmund; Frettlöh, Dirk, "Ammann-Beenker", Tilings Encyclopedia, Bielefeld University Penrose, R. (1997), "Remarks on tiling: Details of a (1+ε+ε2) aperiodic...

of this one dissection. These squares and rhombs are used in the Ammann–Beenker tilings. A skew octagon is a skew polygon with eight vertices and edges...

first two dimensions of the new coordinates produces an Ammann–Beenker tiling (another such tiling is produced by projecting along the last two dimensions)...

topics in tiling theory: colored patterns and tilings, polygonal tilings, aperiodic tilings, Wang tiles, and tilings with unusual kinds of tiles. Each chapter...

the Percolation Thresholds of a Three-Dimensional (Icosahedral) Penrose Tiling by the Cubic Approximant Method". Crystallography Reports. 50 (6): 938–948...

The vertices of the A7 2D orthogonal projection are seen in the Ammann–Beenker tiling....

similar to the 10-fold Penrose rhombic tilings, and 8-fold Ammann–Beenker tilings. The 12-fold tiles easily tile periodically, so special rules are defined...

3,3,5}, called an order-5 tesseractic honeycomb. The Ammann–Beenker tiling is an aperiodic tiling in 2 dimensions obtained by cut-and-project on the tesseractic...