If you cut the cane (of even a wad of scrap) in half and open it like a book with two sides which are the reverse of each other, you have MIRRORD. If you start with TRIANGLES and put six or eight pieces together with "reflections" all around, you have KALEIDOSCOPED. Think about what you see when you look into a kaledoscope. If that's not what your cuts and flips look like, try again! If you do a mirror once, and then cut to mirror a second time going in the same direction, you have made a Natasha bead.