A canonical polygon, as defined by Kyrmse (2021), is a simple polygon whose vertices lie on a square unit
point lattice and whose edges
consist of vertical and horizontal steps of unit length or diagonal steps of length
at odd multiples of 
with respect to the lattice axes. Consecutive sides must
have different directions. Translations, rotations,
and reflections that preserve the lattice
are counted as equivalent. The numbers of distinct canonical polygons of 
, 2, ... sides are 0, 0,
1, 3, 3, 9, 13, 52, 140, 501, 1763, 6785, 25571, ... (OEIS A052436).
There are exactly eight distinct canonical convex polygons, illustrated above.
The construction can also be generalized by rotating the two perpendicular diagonal directions together relative to the lattice axes. In that generalization, the vertices need not lie on the original point lattice.
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.
