I am looking for toys or props that illustrate concepts from abstract algebra. The best known example is of course the Rubik's Cube; another great example is the Fifteen Puzzle, especially if like Sam Loyd you offer $1,000 to any student who manages to switch the 14 and the 15.
There should be many, many more. For example it should be possible to construct a toy that physically illustrates that $S_8$ (say) is generated by a transposition and an $8$-cycle, and I vaguely even remember having something like this when I was a kid, but I have no idea where to get one.
Where can one get such toys or props? I am especially interested in actual, physical toys which I can buy somewhere and use during my abstract algebra course this fall.