For each integer n >= 3, we can create a perfect n-sided polygon in two dimensions. That polygon will have some nonzero spacing between the points, roughly a di

For each integer n >= 3, we can create a perfect n-sided polygon in two dimensions. That polygon will have some nonzero spacing between the points, roughly a distance like 2pi/n. Okay, now that is true for every n >= 3. This means that there are an infinite number of n for which it is true, i.e. an infinite number of polygons. However, each particular polygon has a nonzero length between points. However again, by picking n as large as you want, you can find polygons where this length is as small as you want, as long as it's strictly greater than 0. None of them are zero.