I have 5 points and I want the affine space of those. I also want to describe the convex envelope of the set of points. I searched on google and found how to do the affine space with 3 points. However I'm not so sure about 5 points.
$IE = { A(-4; 2;-8); B(1;-1/2; 2); C(1;-1; 2); D(2;-3/2; 4);E(-1; 0;-2) }$
Now I'm wondering if it looks like $ A = (A-B)+(B-C)+(C-D)+(D-E)$
Or should I made a bunch of vector, I mean, a vector between each points ? $ A = (A-B)+(A-C)+(A-D)+(A-E)+(B-C)+(B-D)+(B-E)+(C-D)+(C-E)$
Then for the barrycenter, I add all my vectors together and / 5. Right ?
Finally, I have to find if the convex envelope to a plan or a line by finding a base of my set A. Any tip ?
Thanks