For example, take the vectors:
$(1,2,3) (4,5,6) (7,8,9) (10,11,12) (13,14,15)$
What would the normal to the polygon be? I'm guessing it would be $(0,0,0)$? For vertices that are linearly independent, you would take the cross product of all adjacent edge vectors, add them up, and normalize the result provided the vertices are ordered in a counter-clockwise direction.
What polygon? You have five points on a line (specifically, the line $(x,y,z) = (t,t+1,t+2)$). You may call their convex hull (i.e., a line segment) a "degenerate polygon" if you want. But that won't help with the normal: there is no concept of normal vector to such a thing.