Besides a square, what regular polygons can be constructed so that the points of that polygon lie on the points of a regular, planar, orthogonal grid?
Besides a triangle and hexagon, what regular polygons can be constructed so that the points of that polygon lie on the points of a regular, planar, triangular grid?
Are there any rules for constructing regular polygons on square or triangular planar grids?
If the points of the constructed polygon are not restricted to grid-points only, but can also include points on intersections of straight lines drawn between existing points, what additional regular polygons can be created on triangular or orthogonal grids?
(No, this is not homework. I was doodling on square graph paper during a meeting and found I couldn't draw a regular octagon referencing only the grid points.)