First time caller here and let me say first, I am not a mathematician, but a science / management writer instead. Today I am very interested in this article, here on the stack:
Spreading points over a triangle plane in 3D space
What I am wondering about is:
As that 3D model is being built (using what appears to be elegant math), can we predict which points of each triangle (A,B,C) connects with the other points of each triangle (a,b,c) when building the 3D sphere illustrated here?
Thx so much for understanding if this is an absolutely inane question :) Jigs
Two faces share an edge if and only if they share two vertices. So let's say you want to determine the coordinates of the points shared by the faces $(A,B,C)$ and $(A,B,D)$. These are simply the points whose coefficient of $C$ or $D$ is $0$; they take the form $\frac{u}{N}A+\frac{N-u}{N}B$.