Many traditional star patterns are built from a plain tiling by the “polygons in contact” method. Mark the middle of every tile edge, send two lines from it into the tile at a fixed angle, and stop each line where it meets the line coming from the next edge. Neighboring tiles mirror each other, so the lines continue straight across, and the stars appear between the tiles. Besides the three regular tilings there are mixed ones, which give the classic 8- and 12-pointed stars and more.