Different angles on the Klein Bottle

A Klein bottle, although appearing bottle-shaped, is an object with a single surface that can take many forms. It gets its name from the man who devised it - Felix Klein (1849-1925) - and from a mis-translation of it's original name. Instead of a Kleinsche Fläche ("Klein surface"), it was called a Kleinsche Flasche ("Klein bottle").

While searching the web for different sized corks, I came across the following picture on the 'ways to mount a Klein bottle' page at kleinbottle.com.

This is not the only way in which a Klein bottle can be 'mounted' - that is, orientated and held up. However, it is the one I somehow find most appealing. (Perhaps the Oxford English Dictionary in the background adds something to the bottle in the foreground.)