Miegakure is a puzzle-platforming game that lets you explore and interact with a 4D world. The fourth dimension in this game is not time, it works just like the first three: it is a mathematical generalization.
You see three dimensions at a time and at the press of a button one of the dimensions is exchanged with the fourth dimension, allowing for 4D movement.
Your ability to move in the fourth dimension in addition to the usual three allows you to perform miraculous feats like seeing inside closed buildings, walking through walls, stealing objects from closed containers, binding two separate rings without breaking them, etc...
These actual consequences of the mathematical formulation of 4D space have been thought about for more than a century (in the 1884 novella Flatland for example) but it is the first time anyone can actually perform them, thanks to the video game medium.
