How do you get the Klein Bottle from two Möbius Strips?

Homework Helper
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Main Question or Discussion Point

...as in the little poem

A mathematician named Klein
Thought the Möbius band was divine.
Said he: "If you glue
The edges of two,
You'll get a weird bottle like mine.

That can be found in the wiki page about the Klein bottle: http://en.wikipedia.org/wiki/Klein_bottle#Properties.

I don't get it.

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HallsofIvy
Homework Helper
...as in the little poem

A mathematician named Klein
Thought the Möbius band was divine.
Said he: "If you glue
The edges of two,
You'll get a weird bottle like mine.

That can be found in the wiki page about the Klein bottle: http://en.wikipedia.org/wiki/Klein_bottle#Properties.

I don't get it.
That's NOT two Möbius bands. That is gluing the edges of one Möbius band together.