Between and Among are NOT only used as prepositions of place. To talk about something done to or by a group or groups of things or people, we can use either between or among:

1- The money is to be divided between/among the towns in the area.
2- The prize will be shared between/among  the first six finishers in the race.


However, when we specify the individual members of the group using singular nouns we use between rather than among:

3- The Treaty of Utricht was signed between Great Britain and Scotland.
4-  There was a disagreement between Ala', Huthaifa and Rami.


We also use between, NOT among, when we talk about comparisons and relationships (e. g. a difference between, a connection between. . ., a friendship between. . ., a link between. . . ):

5- What  are the differences between rugby league, rugby union and American football?
6- They are wrong to claim that there is a connection between unemployment and crime.


We use among, NOT  between, when we mean  "occurring in", "one/ some of" or "out of":

7- The disease has  now broken out among the hill tribes. (= ' occurring in')
8- They are among the best hockey players in the world. (= some of)
9- Among the capital cities of South America, Quito is the second highest. (out of)


Notice how we use the expression among other things ( NOT 'between other things'):

10- Among other things, I enjoy painting and gardening.
11- I later found out that he had been a carpenter and a dustman, among other things.

 
It is I, Odysseus