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. For hexagonal tilings, the Bell shape proved very useful. Depending on the needs of a particular tiling design, a number of supporting shapes were formalized. Follow this link to a page detailing more shapes . I'd gotten to know Miroslav Vicher when he started solving a variety of difficult tiling problems, such as Eternity.