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Hi there acidic llama,
In 3D, when you rotate a face you're turning that face, which is 3x3
pieces, so 9 pieces.
In 4D, when you rotate a cell you're turning that cell, which is 3x3x3
pieces, so 27 pieces.
Visualizing the top cell on the 3^4 as a Rubik's cube is a tiny tiny bit
like visualizing the 3x3 face on the U layer on a Rubik's cube as a
"Rubik's square", which doesn't work well in this case.
You can't exactly think of each cell on the 3^4 as an individual Rubik's
cube, just like how you can't think of each side on the 3x3x3 as
independent from the rest of the puzzle.
Not sure how else to explain this.
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