Games like Portal and Prey have shown that non-euclidean portals are always a good thing to add to an environment. An idea I've had for somewhat longer doesn't involve just portals, but rather an entire world built in more than three dimensions.

The game could start off with the player locked in a house that seems normal for the most part. Interactive physics, a fun little bit of exploration. At some point, the player stumbles across a stairwell, door, or room that violates the laws of ph...