Exploring the impossible landscape of non-euclidean geometry in AR and VR

There are infinite possibilities for world structure inside of a non-euclidean world. One of these ideas that would be impossible to replicate in the physical world is an endless house inside of one room. It is possible with non-euclidean programming to make a room with the space of four rooms only contain three. The fourth room would not become empty, but it would not be created by the program engine. The user would walk through three rooms and end back at the same point as if they had walked four, essentially shortening the distance they walked by one room. The house has not changed size on the inside, the world has just become non-euclidean!