One problem with it, which I thought of before going to sleep, is that the twelve intermediate faces all border on two edges with the number 0. For example, 12 borders on 01/02 and on 10/20. But it could be made to work by substituting another symbol for each of the two zeros, such as Z for the preceding 0 and X (Roman numeral 10) for the trailing 0. Alternately, you could use 7 instead of a trailing 0, which would make all the numbers around a face unique, and then use a different symbol than 00 for the center square. This also has the advantage of numbering each cube in the tesseract. The diagram I made makes it easy to identify the 8 cubes. These are:
One problem with it, which I thought of before going to sleep, is that the twelve intermediate faces all border on two edges with the number 0. For example, 12 borders on 01/02 and on 10/20. But it could be made to work by substituting another symbol for each of the two zeros, such as Z for the preceding 0 and X (Roman numeral 10) for the trailing 0. Alternately, you could use 7 instead of a trailing 0, which would make all the numbers around a face unique, and then use a different symbol than 00 for the center square. This also has the advantage of numbering each cube in the tesseract. The diagram I made makes it easy to identify the 8 cubes. These are: