In the paper Fair Dice, the author describes "face transitivity" as the ability to transfer one face to the position of another and still have the solid look the same (this will ensure it forms a fair die).
When I look for the definition of transitivity on Wikipedia, it says -
Whenever an element a is related to an element b and b is related to an element c then a is also related to c.
I must be missing something obvious, but how is the above related to the ability to swap faces?
A solid is face-transitive (isohedral) when, for any faces, A and B, of the solid, there exists a symmetry of the entire solid, via some reflections and rotations, that maps A onto B.
Well, if there is such a map of A onto B and such a map of B onto C, then there is also such a map of A onto C.