It takes less effort to define it without that restriction, then an octagon is just eight vertices with lines between them.
You can add various restrictions such as not allowing it to intersect itself or requiring that it is convex, but not allowing 3 successive vertices to be colinear doesn't really give you any useful properties so I'm not sure why you'd want that.
You can add various restrictions such as not allowing it to intersect itself or requiring that it is convex, but not allowing 3 successive vertices to be colinear doesn't really give you any useful properties so I'm not sure why you'd want that.