Comments on: Why cubie orientations are preserved
https://php.mandelson.org/mk3/index.php/2022/05/28/why-cubie-orientations-are-preserved/
Mk. III, risen from the ashes of Mk. IISat, 28 May 2022 18:08:44 +0000hourly1https://wordpress.org/?v=5.0.16By: Jacob's blog
https://php.mandelson.org/mk3/index.php/2022/05/28/why-cubie-orientations-are-preserved/#comment-42953
Sat, 28 May 2022 18:08:44 +0000https://php.mandelson.org/mk3/?p=1732#comment-42953[…] Since each turn rotates the edge cubies by 360° in total and every sequence is a composition of face turns, the “total rotation” of all the edge cubies together is a multiple of 360° and so equivalent to 0, meaning there can only be an even number of 180° edge cubie flips. The corner cubie rotations sum the same way, hence the corner cubie rotations that don’t cancel themselves out must sum to a multiple of 360°. The conclusions are correct: no sequence can do an odd number of edge flips or corner rotations that aren’t equivalent to zero. However, the argument is unsound: adding rotations around different axes together willy-nilly like this can (in other contexts) produce complete nonsense — there’s some extra structure in the Rubik’s Cube that makes this OK [for different reasons explained here]. […]
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