Wednesday, 7 February 2007

soft question - Why are the Dynkin diagrams E6, E7 and E8 always drawn the way they are drawn?

I disagree with the universality of your question, but I agree that the diagrams are often drawn in similar ways. They are drawn that way because they are easy to draw that way, and there isn't a good reason to deviate from what we are taught. I have seen both of your proposed alternatives for the $E_6$ diagram in the literature, and I might even say that your first alternative is the most common drawing I've seen.



There are in fact alternative conventions, e.g., if you put a 120 degree angle between consecutive edges, you don't have to spend as much time drawing vertices, and this can be helpful if you have to draw a lot of them, or have difficulty drawing convincing dots. As Guntram noted in the comments, some Wikipedia contributor has found a clever way to compress all of the Dynkin diagrams into a small, unreadable box.

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