Rubik's Tesseract

Have you ever gotten bored once again solving your same old Rubik's cube under the desk during History class? Has it ever gotten a bit repetitive? Well our very numerous scientists and engineers have innovated and added a new dimension to the classic puzzle! Literally! For those of you already used to the 4th dimension and wanting to step further, this game also simulates cubes of higher dimensions, so that you can continue to have fun with cubes with ever more faces by face. Due to computing limitations, this version is sadly currently limited to a maximum of 40 353 607 faces by face. But given proof of solving such a cube, our engineers may find the motivation to allow for even bigger cubes! (Be aware that on normal computers, performances start to suffer at around 100 000 faces by face.) While no release of physical tesseracts and hypercubes are planned, our CEO has heard that people are happily throwing billions around these days, and would happily accept such a financing to get a team working on it. (Successful results not guaranteed) Some may wonder why this game was made. To that I have a few answers, all true in their own way: 1. I just woke up on day with the urge to spread eldritch knowledge upon the unsuspecting. 2. I was unemployed when I got started. Bored engineers get strange ideas, and act upon them. 3. Preparatory school traumatized me, and I had to perpetuate the trauma by inflicting it upon a wide audience. 4. To see if I could (and if it was even possible). 5. This is actually an offshoot from a first person 4D puzzle game, though given I'm a bit ambitious, it is far from finished.