Neat! Are the six permutations on the left an exhaustive list of proper dice patterns, or simply an example?
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Apparently simply an example, last night after posting that I somewhat accidentally came up with two more, one of them being bars on the sides, that are also proper dice!
And if you haven't noticed already, when I find one new dot pattern that works, there's automatically at least two other dot patterns to go along with that.
Edit: And yes, I'm adding those into these crude pixel renders as I find them. I also found another 5/5/5 pattern somewhere along the way...
Update, more organized plus 12 additional puzzles, and a few select isometric examples..