Sources: pensieve.
Abstract. My goal is to get you hooked, captured and unreleased until you find all 17 in real life, around you.
We all know know that the plane can be filled in different periodic manners: floor tiles are often square but sometimes hexagonal, bricks are often laid in an interlaced pattern, fabrics often carry interesting patterns. A little less known is that there are precisely 17 symmetry patterns for tiling the plane; not one more, not one less. It is even less known how easy these 17 are to identify in the patterns around you, how fun it is, how common some are, and how rare some others seem to be.
Gotta Catch 'Em All!
Links. My tilings page, the Conway - Burgiel - Goodman-Strauss book, Conway's lecture, DW, Longtin.
Similar talk with video: Treehouse-1410.