With the interactive diagram above you can generate geometrical figures for scales and chords in 12-tone equal temperament. Have a look at these examples and this page to see how it works. (Best viewed on Firefox.1)
Maybe this can help to illustrate some music theory (or abstract algebra, introducing cyclic groups 😀), I'm not sure. Let me know if you found a nice use case.
1 Chrome adds some ugly extra space before the flat symbol.