Triple Klein Bottle

As the Klein bottle, the triple Jeener-Klein bottle is a non orientable surface (it has only one side, as the Möebius strip). The name of the triple (or more generally multiple) Klein bottle refers to its original inventor, P. Jeener, a French artist and copper engraver specialising in mathematically inspired work (see wikipedia).

The odd multiples of the Klein bottle are all non orientable. The even multiples are orientable. You can have a look to the Quadruple Klein Bottle.