The simple tile shapes that most folks use on their floors end up with a design that repeats itself over and over. A group of mathematicians found a single shape that does not repeat itself when tiled and found the thirteen-sided shape seen below. They call their shape a "hat", but the technical name is "einstein", which means "one stone" in German, not a reference to Albert. So if you're looking for some really wild floor tile patterns, this might be useful, although I have no idea if anyone sells these yet.
More information and a link to their 89-page mathematical proof can be found at the link below.