How to “map” between 3 values?

I have lots of data like this

type1, type2, type3
aax, ert, ddd
asx, eer, kkk
xkk, fff, lll
xxj, vtt, lle
...

and I would really like to be able to "map" between them, so I can go from

type1 -> type2
type1 -> type3
type2 -> type1
type3 -> type1

Example:

type1_to_type2(aax) should return ert
type1_to_type3(asx) should return kkk
type2_to_type3(fff) should return lll
type3_to_type1(lle) should return xxj

What data structure should be used for the data?

And how would such functions look like?

Update: All data is unique.