simply-laced Dynkin diagrams previous next

There's a remarkable correspondence between finite subgroups of SO(3) and simply-laced Dynkin diagrams, called the McKay correspondence.

Find a collection of unit vectors in ℝn that are all at 90° or 120° angles from each other. Draw a dot for each a vector. Draw an edge between dots when their vectors are at a 120° angle. Demand that the resulting graph be connected. The result is a simply-laced Dynkin diagram. For example:










I created the Dynkin diagram here. I hereby release it into the public domain.