Miegakure, a true 4D puzzle-platforming game

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 walk through walls, see i