I am implementing the gift wrapping algorithm to find the convex hull of a set of points in the 3D space.
However, all the articles I have read seem to omit the description of the first step of the algorithm; namely, finding a face (that is, a triangle) in the set that will definitely be in the convex hull (and doing so in $O(n^2)$).
Example of such an article: https://www.sciencedirect.com/science/article/pii/S002200000580056X
I do understand how to find a vertex that definitely be in the convex hull: just take one with extreme coordinates. However, I don’t know how to approach the problem for edges or faces.