Between this, plus the text and illos in the article, does it seem clear where things go and what's supposed to happen?
No, a coordinate system is an address system, and it should provide addresses independently of what it provides addresses to. Suppose I told you that the White House was at WH Pennsylvania Ave. Would that help you find it? WH and BH are not helpful designations, because they do not indicate the relations of these areas to each other or to other areas of the board. Likewise, adding the letter A to some areas has not been helpful. By naming areas of the board after their function in the game, you have left their location obscured, and you have made it more difficult for the reader to understand how the geometry of a tesseract works.
No, a coordinate system is an address system, and it should provide addresses independently of what it provides addresses to. Suppose I told you that the White House was at WH Pennsylvania Ave. Would that help you find it? WH and BH are not helpful designations, because they do not indicate the relations of these areas to each other or to other areas of the board. Likewise, adding the letter A to some areas has not been helpful. By naming areas of the board after their function in the game, you have left their location obscured, and you have made it more difficult for the reader to understand how the geometry of a tesseract works.