Today I read
this article about a new pentagon discovered that can cover a plane perfectly and completely by tiling.
At the bottom of the article, it has this nice picture of all such pentagons discovered so far:

I'd bet you could make a very interesting looking game with tiles of some of these shapes.
(the article also mentions that all triangles and quadrilaterals can tile a plane. Of course, hexagons can too.)
Has anyone ever seen/made a game that explored this idea? I'd imagine that it would get messy when you have to start dealing with pixels, but I still want to see/try it!