I created a Hypercube screen saver back in the day from instructions provided in a Scientific American article, which if memory serves was written by Martin Gardner.
A casual search leads me to believe the article is in his book Mathematical Carnival, though I could be wrong.
https://www.amazon.com/Mathematical-Carnival-Martin-Gardner/...
While you program it up, you can play this little Hypercube game. Do it in 3D, then turn on the 4D to get an intuitive feel for the 4D world.