Imagine a convex hull of n points in $\mathbb{R}^4$. The coordinates of the vertices of the convex hull are as follows:
$$p_a = (a, a^2, a^3, a^4) \ \ \text{for} \ \ a = 1, ..., n$$. I want to prove that the number of faces in the convex hull is at least proportional to $n^2$.
Is it enough to say that each point must have a face connecting with each other point meaning that there are, at a minimum, $n^2$ total faces in the convex hull?