Do you mean a die? As in the singular of dice? I don't think it matters in static geometry, though it probably does if the object had skeletal animation. In any case, there's no point fretting about it. If you want a hard, clean edge between two triangles you can't share vertices and if you want a smooth edge between two triangles, you will want to share verts.
Share them where you can, but don't mess up the shading of objects trying to save a few vertices. It's not worth it.
In your example of a cube, you can share verts between the triangles on each of the six faces, but you can't share them between different faces because then you won't have clean, crisp edges between the faces. ( You'll end up with a squared off sphere instead of a nice clean cube. )
Share them where you can, but don't mess up the shading of objects trying to save a few vertices. It's not worth it.
In your example of a cube, you can share verts between the triangles on each of the six faces, but you can't share them between different faces because then you won't have clean, crisp edges between the faces. ( You'll end up with a squared off sphere instead of a nice clean cube. )