A Socolar tiling is an example of an aperiodic tiling, developed in 1989 by Joshua Socolar in the exploration of quasicrystals. There are 3 tiles a 30ð rhombus, square, and regular hexagon. The 12-fold symmetry set exist similar to the 10-fold Penrose rhombic tilings, and 8-fold AmmannâÂÂBeenker tilings.
The 12-fold tiles easily tile periodically, so special rules are defined to limit their connections and force nonperiodic tilings. The rhombus and square are disallowed from touching another of itself, while the hexagon can connect to both tiles as well as itself, but only in alternate edges.
The dodecagonal rhomb tiling include three tiles, a 30ð rhombus, a 60ð rhombus, and a square. Another set includes a square, a 30ð rhombus and an equilateral triangle.