Convex lattice polygons up to affine unimodular transformations

AGL₂(ℤ) lattice polygon database

The data layer stores normalized vertex lists and source labels. Most invariants are computed in the browser from the vertices, with pointed Fano data shown after choosing an interior lattice point.

General search

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Record ID Source Display limit Normalized volume Vertices Boundary points Interior points Total lattice points

Advanced search

Advanced filters are grouped by type. Metadata-level filters are applied first; exact vertex / lattice-point filters are applied only after the candidate set is reduced. Fraction inputs such as 1/2 are accepted where meaningful.

Combinatorial / Ehrhart data

Ehrhart value #(kP ∩ M)

Lattice / affine geometry

Lattice width Minimum-width direction count Minimum bounding square Dilation factor Primitive polygon normalized volume Primitive polygon boundary points Interior lattice configuration Interior points collinear Minkowski decomposable

Toric fan / singularities

Primitive edges Non-primitive edges Max edge length Min edge length Max normal multiplicity Min normal multiplicity Number of singular cones Edge length cycle Normal multiplicity cycle Smooth fan All edges primitive K_X Cartier index Gorenstein fan (K_X Cartier) Has reflexive interior origin Torically minimal smooth fan Class-group torsion order (-K_X)^2 Fano index (free part) Number of smooth cones

Algebraic topology / surface proxies

Adjoint-tower depth Canonical polygon vertices

Symmetry / exact cycles

Centrally symmetric Affine automorphism group order Orientation-preserving automorphisms Orientation-reversing automorphisms Has nontrivial symmetry Has reflection / orientation reversal Symmetry group type

Exact cyclic sequence filters are in the toric group. Central symmetry uses the fast metadata flag; automorphism-order and symmetry-type filters are verified from the polygon vertices.

Idle.

Results 0

Drawn polygon search

Click lattice points, compute a convex hull, then match up to GL₂(ℤ).

Search results will appear here, directly under this title.

Grid size

Click actual lattice points to select/cancel them. The convex hull is recomputed immediately inside the same grid.

No points selected.

About this build

This version uses a fast metadata layer for search, lazy-loads vertex chunks only when a record is opened, and keeps calculations close to the vertex data. Some global AGL₂(ℤ) canonicalization and all-record merging remain conservative by design; drawn searches and adjacency navigation perform stricter equivalence checks on narrowed candidate sets.

AGL2(ℤ) lattice polygon database

General search

Results 0

Drawn polygon search

About this build

AGL₂(ℤ) lattice polygon database