Are palindromic triples of roots of any interest in algebraic group E6?

Question

Consider the 72 roots of the algebraic group E6 in their most symmetric coordinatization (in 9-space), as given in the section "Roots of E6" here:

https://en.wikipedia.org/wiki/E6_(mathematics)

From these roots, we can clearly form ordered palindromic triples of roots RiRjRk where Ri is the same root as Rk.

Are such ordered palindromic triples of roots of any particular interest in E6 or structures derived from E6?

If so, where and why?

Thanks for whatever time you can afford to spend considering this question.