What is the difference in the meaning of the following sentences: 
 
>> "I found the map, but one of its corners had been **torn away.**"

>> "I found the map, but one of its corners had been **torn off.**"

>> "I found the map, but one of its corners had been **torn down.**"

>> "I found the map, but one of its corners had been **torn apart.**"

Does **"torn away"** means that the corner of the page was torn apart/down and then it was lost?