Later, we filed a patent on the system. Patent 4133152 is the Penrose Tiling system. Used with permission. In addition to discovering a variety of squares, we also found hexagons and dodecagons. This feature allows tile to be laid with much less cutting.
Hexagonal layouts are possible with many patterns.
Used with permission. I'd gotten to know Miroslav Vicher when he started solving a variety of difficult tiling problems, such as Eternity. After Adrian and I filed the patent, we hired Mira to look for solutions with this system using his program, and he found thousands. Dolook at Miroslav Vicher's site , for more. For example, the following is one of over ten thousand dodecagon patterns he found.