[trakl]

While it can be useful (or not) on the applications described, this is not non-euclidean. It is pure euclidean, but defined in steps.

I agree that is visually exciting and all that jazz, but this has nothing to do with Non-Euclidean Geometry... My surprise is that I though this video will give some 3D intuition on this topic, but nay.

[adrusi]

This is noneuclidean, in that it violates the axioms of euclidean geometry.

1. A straight line may be drawn between any two points.

2. Any terminated straight line may be extended indefinitely.

3. A circle may be drawn with any given point as center and any given radius.

4. All right angles are equal.

5. If two straight lines in a plane are met by another line, and if the sum of the internal angles on one side is less than two right angles, then the straight lines will meet if extended sufficiently on the side on which the sum of the angles is less than two right angles.

It follows from those axioms that the sum of the angles of any triangle is 180°, but in that 3-room house, for instance, you could draw a triangle with 3 right angles, so it must violate the axioms.

[zenorogue]

The phrase "non-euclidean geometry" does not mean "any geometry that violates the Euclid axioms" but specifically that the parallel postulate is replaced. traki is right.

[trakl]

I've got to reconsider given adrusi's comment, I think he's actually right. The parallel postulate is what makes the sum of angles of any triangle to be 180º.

[zenorogue]

Other Euclid's axioms should still hold in non-Euclidean geometry, but with portals and walls, they do not. Mathematicians who are experts in non-Euclidean geometry would agree that portals do not yield non-Euclidean geometry, e.g. Henry Segerman http://twitter.com/henryseg/status/970797060369846273 (see also http://twitter.com/marctenbosch/status/301331439725719552 ).