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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.

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  • $\begingroup$ A square nicely illustrates $D_8$. $\endgroup$ – Chris C Aug 13 '14 at 14:33
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I have the answer for you: Reptangles: turtles that snap. These are little plastic turtles which allow connections in a bunch of different ways. Like legos, but more possible angles. The end result is you can assemble shapes with all sorts of symmetries. You also have color to help illustrate your point. Here's a picture: enter image description here

The instructions have a fair amount of symmetry discussion built-in, I have the feeling a math person designed these, but it's just a hunch. My 6 year old also loves to play with them and I got him some at home just as a toy (for now, I mean I don't expect abstract algebra until middle school ;)

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