Escher reptile tiles all fit together (tesselate) like this. Two lizards rotate 120 degrees on each of 3 rotation points, one clockwise and one counterclockwise.The 6 lizards fit in different spaces of the central lizard. The repTiles can go on forever, here we only show 7 tiles.
My wife Kathy painted this pattern over top of Escher's original reptile tile. Note that lizards face in one of 3 directions. There's an underlying order 3 symmetry as well as a hexagonal motif. The curve of 3 of the 6 sides of the hexagon are simply inverted versions of neighboring sides. So there's an underlying hexagon and also a triangle of rotation points. Each lizard intersects with 6 lizards, just as a hexagon intersects with 6 other hexagons.
