WHAT ARE THESE SHAPES, ANYWAY?

MÖBIUS STRIP

(fig. 2)

Known as the ‘twisted cylinder’, the Möbius strip is a one-sided, non-orientable surface. In other words, it’s a shape that, if you trace a line along it, will bring you back to the mirror image of your starting point (that initial point’s reflection on a 2D coordinate plane). You can make your own Möbius strip if you give a strip of paper one half-twist and tape the ends together to form a continuous loop. Most simply of all, a Möbius strip is essentially the infinity symbol manifested in 3D space.

KLEIN BOTTLE

(fig. 3)

The Klein bottle is a type of non-orientable surface that is impossible to consistently plot in a two-dimensional space. And because it is a one-sided surface, you will gradually flip upside down while travelling along it.

Unlike the Möbius strip, though, it has no boundaries.

– Courtney Linder