Q:

How many foci does a converging or diverging lens have? 

I thought this was a simple question but can't seem to find a direct answer. 
In ray diagrams with a converging or diverging lens, we always draw F (the focal length) on both sides of the lens.  But the focal point for any thin lens is only one, isn't that right?  The point at which light converges or appears to converge.  
Or is it two, depending on different situations... such as objects placed behind or in front of the lens? 
What do we officially say?  Does a lens have two foci or one? 

A:

A lens is symmetric.  By this I mean you can pick it up, turn it round and put it back and the light rays don't change.  Or to look at it another way, it doesn't matter whether the light travels from left to right through the lens or right to left. 
So parallel light travelling from infinity on the left of the lens will converge at the focal point on the right.  Likewise parallel light travelling from the right of the lens will converge at the focal point on the left. 

So in this sense a lens has two focal points - one on each side.