I replaced the zeros on Black's cube with sevens; the trailing zeros were throwing off even more patterns than what you describe.
Okay, I've modified my tesseract image to use 7 instead of a trailing 0. This has the effect that each cube in the tesseract consists of all the faces with the same digit, which makes it easy to designate each cube with that same number, and each face designation is a combination of the numbers belonging to the two cubes which share that face. So, there are two ways of designating a face that give the same result in a convenient circling back kind of way.
Okay, I've modified my tesseract image to use 7 instead of a trailing 0. This has the effect that each cube in the tesseract consists of all the faces with the same digit, which makes it easy to designate each cube with that same number, and each face designation is a combination of the numbers belonging to the two cubes which share that face. So, there are two ways of designating a face that give the same result in a convenient circling back kind of way.