Try to wrap your brains around this little animation:



Hypercube, or a Tesseract is “the four-dimensional analog of the cube, just as the cube is the three dimensional analog of the square.”

Now the same model performing a double rotation about two orthogonal planes:



And then there is “24-cell convex regular 4-polytope performing a double rotation about two orthogonal planes.” Ready?

Here it comes (don’t stare at it too much):



For the science fiction treatment of Hypercube, read a classic story “And He Built a Crooked House” by Robert A. Heinlein – click here.