Computers are perfectly happy to model objects in higher dimensions.
The 3D objects can easily be understood by rotating them around on the screen. You can do that by clicking the left button of the mouse in the window and dragging the mouse around with the button held down. Even so, it is quite possible to gain a strong feeling for the 3D projections that result from some operations on 4D objects. Every feature of the original puzzle has an analogy in four dimensions. For the rest of this document, those features will be in double quotes when we are talking about higher dimensional analogies.