I’m working on developing a 3-D convex hull algorithm in Mathematica for the 4-colour rhombohedral lattice. Right now I’m trying to grasp how to store the connectness or topology of the convex shell.

I have an ordered list of vertices. I need an adjacency matrix, which indicates which vertex is connected to which other vertex. A web reference for this is:
http://en.wikipedia.org/wiki/Adjacency_matrix
(original link, which was no longer available, replaced 20 May 2012)
A great thing about the adjacency matrix is that it incorporates the direction of each connecting link. This allows me to distinguish between a forward link and a backward link.