If you itch to add a 3rd axis to turn a 2x2 into a 2x2x2, you basically don't get why the game is being played at all
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booo. Lots of great 3 axis typologies. Now, if you push that to four, well that's absurd.
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Your despicable tri-bal kind may rule in the VR future though, but the noble ones will always remain 2d
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:) note, I do think the affordances of paper probably is one of the main reasons why the 2x2 dominates. And bounded rationality.
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