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

[quasar987]

...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.

 

[quasar987]

Never mind, I found a nice picture illustrating said gluing: http://en.wikipedia.org/wiki/Mayer–Vietoris_sequence#Klein_bottle

 

[HallsofIvy]

...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.