Möbius strip or sheet - a surface which is formed by bonding a rectangular sheet so that opposing vertices are connected.
This is a non-orientable surface, which is one-way, ie, when moving across the surface without crossing the boundaries, it can be a starting point, but on the other side of the sheet.
Take an elongated strip of paper rectangular ABB1A1.
Fold the sheet so as to coincide with the vertex A vertex B1, B and the vertex coincides with the vertex A1. Glue the ends of the sheet, the resulting surface will be a sheet of Mobius.
The resulting tape does not fall apart if it is cut at the middle line, it will turn into a one-sided, double-twisted surface.
If we continue to cut two or more twisted sheets, then there are more amazing pieces such as "trefoil knot" or "Paradromnye ring."
If you glue the two Möbius strip together along the edges, you get a figure, called "Klein bottle". In a typical three-dimensional space to build it is impossible without self-intersections.