In mathematics, the Klein bottle is an example of a non-orientable surface; that is, informally, a one-sided surface which, if traveled upon, could … See more

Dissecting a Klein bottle into halves along its plane of symmetry results in two mirror image Möbius strips, i.e. one with a left-handed half-twist and the other with a right-handed half … See more

The figure 8 immersion
To make the "figure 8" or "bagel" immersion of the Klein bottle, one can start with a Möbius strip and curl it to bring the edge to the midline; since there is only one edge, it will meet itself there, passing through the midline. … See more

The following square is a fundamental polygon of the Klein bottle. The idea is to 'glue' together the corresponding red and blue edges with the … See more

Like the Möbius strip, the Klein bottle is a two-dimensional manifold which is not orientable. Unlike the Möbius strip, it is a closed manifold, meaning it is a compact manifold without … See more

One description of the types of simple-closed curves that may appear on the surface of the Klein bottle is given by the use of the first … See more

Regular 3D immersions of the Klein bottle fall into three regular homotopy classes. The three are represented by:
• the "traditional" Klein bottle;
• the left-handed figure-8 Klein bottle;
• the right-handed figure-8 Klein bottle. See more