The faces of these two cubes do not count as faces of the tesseract, but the quadrilateral shapes that extend between the larger and smaller cubes are the faces of the tesseract
I think this is incorrect. The faces of the two cubes are 2d faces of the tesseract. E.g. the faces numbered 1 and 2 in the first diagram (the slant of the font helps identify where the numbers are supposed to be.)
Numbering the cube like a die, the faces of the tesseract are 1-2, 1-3, 1-4, 1-5, 2-1, 2-3, 2-4, 2-6, 3-1, 3-2, 3-5, 3-6, 4-1, 4-2, 4-5, 4-6, 5-1, 5-3, 5-4, 5-6, 6-2, 6-3, 6-4, and 6-5.
I'm not positive I understand what you're describing here, but I think 1-4 and 4-1 are the same face. And the ones you're missing are two copies (one from the large and one from the small cube) of say "1" (1-1? 1-0?) through "6". (While 1-6 indeed doesn't exist.)
I think this is incorrect. The faces of the two cubes are 2d faces of the tesseract. E.g. the faces numbered 1 and 2 in the first diagram (the slant of the font helps identify where the numbers are supposed to be.)
I'm not positive I understand what you're describing here, but I think 1-4 and 4-1 are the same face. And the ones you're missing are two copies (one from the large and one from the small cube) of say "1" (1-1? 1-0?) through "6". (While 1-6 indeed doesn't exist.)