A Penrose tiling (Wikipedia), named for British mathematical physicist Sir Roger Penrose, who investigated them in the 1970s. A Penrose tiling is “aperiodic,” or, simply put, produces a pattern that does not repeat itself no matter how far you extend it across the plain. All Penrose tilings are aperiodic, but not all aperiodic tilings are Penrose tilings.
Lots of bright creative folks have installed custom Penrose tile floors. Here’s a selection of a few of my faves from around the web. I couldn’t find anybody online who’s selling pre-cut Penrose prototiles, so it looks like anybody who wants to do it themselves has to cut their own. Or, if somebody is feeling entrepreneurial…