Background on this GlassEye stained glass pattern: In some ways the pattern here, the Cartwheel, is the most important Penrose Tiling. The purple region at the center is outlined by a decagon consisting of a kite and dart edge. Every point in every tiling is contained inside an identical decagon (although the contents may differ.) The outer portion of the pattern consists of two parts. There are ten yellow (here I have used gold & purple) sectors and ten blue spokes. The spokes consist of "bowtie" units and the spokes can be flipped 180 degrees and still fit their adjacent sectors. That means there are 1024 possible spoke arrangements, but after rotations and reflections are eliminated there are only 62 distinct patterns. Each of the spokes can be continued inside the cartwheel, but eventually they end, enclosing a region that Penrose calls a "decapod." All decapods can be constructed out of 36-108-36 isosceles triangles. The one shown here, dubbed "Batman," (in red, except for Batman darts in black,) is the only one of the 62 decapods that can be legally tiled with darts and kites. The five darts in a Batman figure and the two intervening kites are the only tiles in any Penrose tiling that are ever part of a pattern without five-fold symmetry. Learn more about the Penrose tilings here To save this cletic stained glass image to your computer right click Click here to view this stained glass pattern in B&W |
