For reasons I wanted to see how many games there are which use Non-Euclidean geometry consistently. i.e. the main game world is constructed around Non-Euclidean space, not only used as part of a mini game or as a 'dream sequence'.

I could not think of many... there are:

Antichamber
HyperRogue
Unseen Diplomacy
The Bridge

and then?

Fragments of Euclid
DmC
Realm of Impossibility, aka Zombies.
Illusions (Collovision)

Addendum :
1 - All tile based games, such as DROD, could be argued to be non-euclidean (see Starmakers post #23 and b_smith_81 #36). As such I will only acknowledge that this is true, and that this list would be huge if I started to add all tile based games. I could put forward that Starmakers point is not about non-euclidean geometry, but rather non-euclidean movements... However, I do acknowledge their points

what do you mean by using n-e geometry?

http://dukenukem.wikia.com/wiki/Lunatic_Fringe Edit: okay, on re-reading the first post this probably isn't what was wanted. It's a capability of the engine but not one often seen.

Fragments of Euclid : https://www.youtube.com/watch?v=mEVTMlz0ZRE

Gorogoa

You don't control any character yourself, but still, the way it deals with space and time is very interesting.

I don't know about non-euclidean, but as for games with very strange geometry, behold one of the best video game levels ever conceived! https://youtu.be/OF7aIWxfgnA?t=284

DmC (reboot) uses some incredible geometry and physics in its alternate world. Not a dream sequence as most of the game happens here. So I guess that could count.

Descent 1+2, not the main games, but there are quite a few mods featuring it.

The old C64 game Realm of Impossibility, aka Zombies.

Euclidean geometry is more or less what we call 'normal' geometry, based on the principles founded by the Greek mathematician Euclid. This is things like parallel lines will never cross, the angles in a triangle adds up to 180, a box have 6 sides and so on.

So Non-Euclidean geometry are those games which do not follow those ''rules'. This can be from subverting them (as Anitchamber does, a cube can have more than 6 sides, parallel lines cross, lines have different length depending on direction and so on) or the game is based on non-euclidean shapes (such as HyperRogue, which is based on hyperbolic planes). I almost put Gorogoa up there myself to begin with, but decided not to. The reason is

Gorogoa is a very, very clever game, but what it does is that it always change your frame of reference. However, within each of these frames, the game world is very much based on euclidean space (as well as normal time). The game then just 'freeze' this frame and transport it from its context into another where it then 'unfreeze'.

aye. I have seen those, but not putting them up as the game itself do not.

One question:

Suppose we have a game with doors that connect certain areas. Suppose further that there's a door that connects A to B, but if you go back through the door after reaching B, you end up at C instead.

Does this count as non-Euclidean for the purposes of this topic?

(There are many games where this sort of thing happens at some point.)

why have I never come across this? I want to play it now The best level from one of the best games ever made. It is euclidean, though. Never played it, so have to take your word for it . Got it somewhere on Steam, but it is not my cup of tea and have always had something more interesting to try... In what way?
no, because the game world is still euclidean. it is just a form of cheating.

What if said doors (or mechanics that act like doors) are the only form of movement in the game?

For example, imagine the game being something like a text adventure, or perhaps one of the more direct descendants of that genre (for example, NES Shadowgate). The game consists of rooms, and you can go between them. But now make it so that movement between the rooms doesn't work as one would usually expect; going north then south wouldn't take you to the same room you were just in. (Note that, in this type of game, there is no such thing as movement *within* a room; the only way to move is to go to another room.)

Could that qualify?