Subject: how can a particle have a spin of 1/2

so i was reading Stephen Hawking's "The universe in a nutshell" and i got to 
the part where he's describing spin.  he says (and i whole heartedly believe) 
that particles exist that if you look at them, then rotate them 360 degrees, 
they will not look the same.  he further says that if you rotate them 360 more 
degrees, they will look the same as they did when you first looked at them.  
now i understand we are talking about quantam particles smaller than photons so 
you can't actualy "see" them, but i still can't get my mind around this idea.  
how is it posible to rotate something that does not change shape (i assume 
prof. Hawking does not seem to say) and have it not look the same when it gets 
all the way 'round.

Re: how can a particle have a spin of 1/2