One alternative, though, which you may find more symmetrical, would be to use 10, 20, 30, 40, 50, and 60 instead of 11, 22, 33, 44, 55, and 66. This would be an exception to the rule of writing the lower digit first. I think this would also simplify the rules for which faces are adjacent. Two faces would be adjacent if they share only a single digit, and the two digits that are different are not on the opposite sides of a die.
I did a preliminary sketch (nothing worth posting) of the diagram with this change, taken from a different projection of a tesseract, and the elegence is very appealing. I also used the same projection for my current letter-code version, and while it's not really any less elegant it is definitely less legible.
I did a preliminary sketch (nothing worth posting) of the diagram with this change, taken from a different projection of a tesseract, and the elegence is very appealing. I also used the same projection for my current letter-code version, and while it's not really any less elegant it is definitely less legible.
I'll put both up tomorrow morning.