As defined by Kyrmse, a canonical polygon is a closed polygon whose vertices lie on a point lattice and whose edges consist of vertical
and horizontal steps of unit length or diagonal steps (at angles which are multiples
of
with respect to the lattice axes) of length . In addition, no two steps may be taken in the same
direction, no edge intersections are allowed, and no point may be a vertex of two
edges. The numbers of distinct canonical polygons of , 2, ... sides are 0, 0, 1, 3, 3, 9, 13, 52, 140, 501, 1763,
6786, 25571, ... (OEIS A052436).

There are exactly eight distinct convex canonical polygons, illustrated above.

The concept can also be generalized to diagonals rotated with respect to the lattice axes.

Note that this mathematically recreational use of the term "canonical" is completely unrelated to the mathematically established concept of canonical
polyhedra as applied to dual polyhedra and
midspheres.