Don't ask me how this mind melting tile trick works, I'm still trying to work that one out.
This YouTube video by Buenos Aires magician Norberto Jansenson achieves the seemingly impossible. Jansenson starts with a grid of tiles that fits perfectly into a frame. As he rearranges the tiles, which are diagonally cut in certain places, he's able to remove a tile without changing the shape of the overall grid. He's able to repeat the mind-melting trick three times over, each time removing another square without changing the shape of the grid. Then, he reverses the trick, re-adding the squares into the frame, one at a time, again without changing the overall shape of the grid.