0

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

enter image description here

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

Hero Jig
  • 9

1 Answers1

0

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 $\frac{u}{N}A+\frac{N-u}{N}B$.

Chris Culter
  • 26,806
  • Thx do much for that Chris! So, there must be a calculation for plotting out each of these then as well: tetrahedron, cube, octahedron, dodecahedron and icosahedron. Also, to create these shapes, does A and B always have to have the same length to form each? Or is that what is meant by irregular if they don't? Thx again! – Hero Jig Feb 08 '19 at 07:53