Polygon used for every ruling
vertical
v = (0,1)
Polygons with one interior lattice point
The sixteen lattice-equivalence classes of convex polygons with exactly one interior lattice point. Select a polygon to see all rulings in genera 0 and 1.
Choose a Newton polygon
Coordinates are centered at the unique interior lattice point (0,0).
Rulings
| Genus | All-disk | Annular | Total |
|---|
Ruling polynomial
RΔ(z) =
—
RΔ(z) =
∑g
rΔ,gz2g,
where rΔ,g is the total number of
genus-g rulings.
These diagrams come from direct ruling certificates. No tropical count or previously known answer is used. The disk/annular split belongs to the displayed torus realization.
Every ruling for this entry uses exactly the polygon and the fixed Λ shown above. Annular eyes are normalized only in lifted coordinates and then mapped back.