Rational polygons database
?The smallest k such that kP has integral vertices.
?Show all k-rational polygons, i.e. also those whose denominator is a divisor of k.
?The number of points of (1/k)ℤ² on the boundary of P, where k is the denominator of P.
?The period divides the denominator. Polygons with period 1 have an Ehrhart polynomial.
?The group of affine unimodular transformations mapping P to itself: Zn is cyclic of order n, Dn is dihedral of order 2n.
?Only for polygons with exactly one interior lattice point: taking it as the origin, the vertices of kP are primitive, where k is the denominator. Then kP is an almost k-hollow LDP polygon, corresponding to a 1/k-log canonical toric del Pezzo surface.
?No strictly larger polygon with vertices in (1/k)ℤ², where k is the denominator of P, has the same number of interior lattice points.
?The dimension of the convex hull of the lattice points of P, or −1 if P contains none.
?The dimension of the convex hull of the interior lattice points of P, or −1 if there are none.
?Polygons that are equivalent to a subpolygon of [0, m]², for the m entered.
?Polygons that can be realized in ℝ × [0, 1]. There are infinitely many of them for each denominator, so some classifications exclude them. See also the coverage page.

498,143,549 polygons.

Incomplete: no denominator is given.