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The Dynkin diagram of the root system of affine $D_4$ is $$ \circ \quad \circ \quad \circ \quad \circ \\ \circ $$ where all of the four vertices in the first row connects to the vertex in the second row.

Is there are root system which has the following Dynkin diagram? $$ \circ \quad \circ \quad \circ \quad \circ \quad \circ \\ \circ $$ where all of the five vertices in the first row connects to the vertex in the second row.

If yes, what is the name of the root system? Thank you very much.

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    $\begingroup$ The corresponding Coxeter group is paracompact and hyperbolic. Apparently it's called $\overline{L_5}$ and it's mentioned here: en.wikipedia.org/wiki/… $\endgroup$
    – Adam P. Goucher
    Commented Jul 26, 2020 at 14:12
  • $\begingroup$ See $E5$ in en.wikipedia.org/wiki/Dynkin_diagram . $\endgroup$
    – user64494
    Commented Jul 26, 2020 at 16:40
  • $\begingroup$ @user64494, I think it is $\overline{L_5}$ in Adam P. Goucher's comment. $\endgroup$
    – Jianrong Li
    Commented Jul 27, 2020 at 6:53

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