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here is an e8 root system

http://upload.wikimedia.org/wikipedia/commons/thumb/f/fe/E8_graph.svg/500px-E8_graph.svg.png

here is some of my root system. the prime roots in mine form essentially the same patterns that are showing up in root systems. Zoom in if needed.

http://2.bp.blogspot.com/_u6-6d4_gs...AAAE8/_hov_b0sno4/s1600/prime-+square+12a.png

also a pdf

https://www.physicsforums.com/attachment.php?attachmentid=31636&d=1296068205