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The fibres of the Scott map on polygon tilings are the flip equivalence classes

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Figure

Fig. 1 a Tile with strand segments; b tiling with strands; c induced plabic graph
Fig. 3 Tilings of the pants surface. Here κ(S, M) = 6 × 0 + 3 × 3 + 2 × 0 + 3 − 6 = 6
Fig. 4 Composing tiles and strand segments. Here τ(d)(2) = 6
Fig. 5 Tilings of an octagon, and the associated Tr(Ti). Note that T1, T2 are triangulated-part equivalent,but T3, T4 are not
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