(0,100)(100,0) (50,0)(50,100) (0,50)(100,50) (0,0)(100,0)(100,100)(0,100)(0,0) (10,10)[0.04in]{} (20,80)[0.04in]{} (30,70)[0.04in]{} (40,40)[0.04in]{} (60,60)[0.04in]{} (70,30)[0.04in]{} (80,20)[0.04in]{} (90,90)[0.04in]{}

&

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&

(0,0)(100,100) (20,20)(100,20) (20,20)(20,100) (25,75)(100,75) (70,70)(70,0) (0,0)(100,100) (0,100)(100,0) (50,0)(50,100) (0,50)(100,50) (0,0)(100,0)(100,100)(0,100)(0,0) (20,20)[0.04in]{} (25,75)[0.04in]{} (70,70)[0.04in]{} (60,10)[0.04in]{}

The column and row signs essentially specify an order in which the monotone entries in a cell of a gridded permutation should be read. Cells corresponding to $M_{k\ell}=f_kg_{\ell}$ are read from left to right (respectively right to left) if $f_k=1$ (respectively $f_k=-1$) and bottom to top (respectively top to bottom) if $g_{\ell}=1$ (respectively $g_{\ell}=-1$). These directions are sometimes marked on our diagrams. The [*base point*]{} of a cell is the corner from which its reading begins.

To describe the encoding of ${\operatorname{Geom}}(M)$ we introduce a *cell alphabet* $\Sigma$ associated to $M$ which consists of a unique letter $a_{kl}$ for each nonempty cell $C_{kl}$ of the standard figure of $M$. Then, to every word $w=w_1\cdots w_n\in\Sigma^\ast$ we associate a permutation ${\varphi}(w)$. First we choose arbitrary distances $$0<d_1<\cdots<d_n<1.$$ For each $1\le i\le n$, we choose a point $p_i$ corresponding to $w_i$ in the following manner. Let $w_i=a_{k\ell}$; the point $p_i$ is chosen from the line segment in cell $C_{k,\ell}$, at infinity-norm distance $d_i$ from the base point of this cell. Finally, ${\varphi}(w)$ denotes 