I worked out what was the actual problem with your diagram: not enough connections.
I've noticed that while working on a PHP script for drawing a similar diagram.
If I got this right,
As I recall from your original description of the 1-24 system, White started on 1, and Black started on 24, which were 11 and 06 in my schema. So, White started on the outer cube, and Black started on the inner cube.
So that you could start White and Black at the extreme ends of the range, I proposed starting White on the inner cube and Black on the outer. This would make no difference to gameplay, but it would let you start White on 01 and Black on 66, which is what you have depicted here.
then it does have an unacceptable asymmetry: Black's connections along the inner cube are all double digits, while White has different digits on all eight of its neighbors.
The double digits are for the outer cube, not the inner one. Being bigger, the outer cube uses bigger numbers. I don't find the asymmetry unacceptable. I wanted the labels to clearly reflect the numbers on a die while being distinguishable. Preceding the number with 0 doesn't change its value, and preceding it with itself doesn't add an extraneous element. 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've noticed that while working on a PHP script for drawing a similar diagram.
As I recall from your original description of the 1-24 system, White started on 1, and Black started on 24, which were 11 and 06 in my schema. So, White started on the outer cube, and Black started on the inner cube.
So that you could start White and Black at the extreme ends of the range, I proposed starting White on the inner cube and Black on the outer. This would make no difference to gameplay, but it would let you start White on 01 and Black on 66, which is what you have depicted here.
The double digits are for the outer cube, not the inner one. Being bigger, the outer cube uses bigger numbers. I don't find the asymmetry unacceptable. I wanted the labels to clearly reflect the numbers on a die while being distinguishable. Preceding the number with 0 doesn't change its value, and preceding it with itself doesn't add an extraneous element. 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.