\begin{tikzpicture}[x=1.18mm,y=1mm,scale=1.6]
    % node numbering is from Tamari's thesis
    % parenthesization is reversed
    % https://www.math.wustl.edu/~escobar/pdf/Olivetti2015.pdf
    \tikzset{every node/.style={scale=.8}}
    \tikzset{>=stealth}
    \tikzset{mm/.style={execute at begin node=$\displaystyle, execute at end node=$}}
    \draw[mm] %objects
    (-7.3,-1.6) node (1120) {\cdot} %{((a(bc))d)e}
    (7.3,-1.6) node (1210) {\cdot} %{(a((bc)d)))e}
    (0,20) node (3010) {a((bc)(de))}
    (0,-19) node (1201) {((ab)(cd))e}
    (-16,1) node (2011) {((ab)c)(de)}
    (16,1) node (2200) {a((b(cd))e)}
    (-11.5,12) node (2020) {(a(bc))(de)}
    (11.5,12) node (2110) {a(((bc)d)e)}
    (-12,-11) node (1111) {(((ab)c)d)e}
    (12,-11) node (1300) {(a(b(cd)))e}
    (0,15) node (4000) {a(b(c(de)))}
    (0,-5) node (2101) {(ab)((cd)e)}
    (-5.5,5) node[transform canvas={xshift=2}] (3001) {(ab)(c(de))}
    (5.5,5) node[transform canvas={xshift=-2}] (3100) {a(b((cd)e))}
    ;
    \path[->,dashed, color=black!50!white]
    (1111) edge (1120) 
    (1120) edge (1210)
    (1210) edge (2110)
    %
    (1120) edge (2020) 
    (1210) edge (1300) 
    ;
    \path[->]
    (2011) edge[shorten >=-1.8] (3001)
    (2200) edge[shorten >=-1.8] (3100)
    (1201) edge (2101)
    (3010) edge (4000)
    %
    (2101) edge (3001)
    (3001) edge (4000)
    (2101) edge (3100)
    (3100) edge (4000)
    ;
    \path[->] %arrows
    (2110) edge (3010) 
    (2020) edge (3010)
    %
    (1111) edge (1201)
    (1201) edge (1300)
    %
    (1111) edge (2011)
    (2011) edge (2020)
    %
    (1300) edge (2200)
    (2110) edge (2200)
    ;
\end{tikzpicture}