It is mathematically provable that 4D shapes exist, but the more I tried to think about this concept, the more frustrating it became. Take the example of a tesseract. A square has two edges at each corner, a cube has three, similarly a tesseract has four. We know that in the same way that a 3D carton can be unfolded into a 2D net with 6 sides, we would be able to perceive an unfolded 4D tesseract as 8 cubes in net with the same 2D footprint. Trying to visualise putting it back together is a f...