Start with a rectangle. A rectangle has 4 EVEN vertices,one at each of the 4 corners for there are two lines coming together at each of the 4 corners, and 2 is an EVEN number. Now if we add a curved line at the top and another at the bottom as shown below, there will be three lines coming together at each corner. And since 3 is ODD, these 4 corners of the rectangle are now 4 ODD vertices: Edwin