Iterating Cube Vertices, Edges and Faces

This keeps haunting me. There must be an awesome way to arrange the data so that you can do a simple for loop and iterate over all cube vertices, edges and faces. I'm sort of after something you could use in matching cube like algorithms to fetch data from a sample grid without having to use lookup tables.

Vertices or sample offsets are easy:

    for (int i = 0; i < 8; ++i)
    {
        const int dx = i & 1;
        const int dy = (i>>1) & 1;
        const int dz = (i>>2) & 1;
        printf("%d: %d,%d,%d\n", i, dx,dy,dz);
    }        

Assuming that you have 3 values per sample, one along each axis, the following code can be used to walk through all the valid edges:

    for (int i = 0; i < 12; ++i)
    {
        const int ax = (i >> 2) & 3;
        const int as = (4-ax) >> 2;
        const int bs = (5-ax) >> 2;
        const int v = ((i&1) << as) | ((i&2) << bs);
        printf("va=%d vb=%d  dir=%c\n", v, v|(1<<ax), "XYZ"[ax]);
    }

But... I'm not satisfied, there must be a cleaner way.

I once figured out how to procedurally draw a cube with just one for loop, but I cannot remember how to do it anymore, IIRC it used rotating sequence of XYZ, ZXY, YZX somehow, much like how you calculate cross products.