https://www.youtube.com/watch?v=W-sKLN0VBkk

I think it is a model of the Projective plane

Technically the crosscaped-disk: http://mathforum.org/mathimages/index.php/Cross-cap

The cross-cap just refers the feature of identifying the sides of a circle in a manner like in the Projective plane.

It is like a Moebius strip (whose width can be made arbitrarily small, even 0), because a Moebius strip with a disk attached to its boundary gives a Projective plane