for example you are sampling a texture on a triangle(2D or 3D) it will always just use a 2D texture. So I am just wondering, why is there an R coordinate? I think S and T would be enough in many cases
I believe you are only considering a single layer with a single texture on all 6 sides on a cube ( 4 sides on a triangle ) ?
If you are using a layered texture, 1 - for graphic or color, But then you want to add wording or pictures, such as Cave Man Drawings, A different one on each side of your cube, Then you need the "R" value included to place those textures on the correct location.
I hope I explained that correctly!