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Re:The Mathematics of the Rubik’s Cube (2009) [pdf] by Retric on Tuesday February 12, 2019 @12:37AM (#19141315)
What you’re describing falls under rotational symmetry.

Rotating top side left one is the same as rotating bottom 2 sides right.

But, more generally limiting rotations to 90 degrees slows things down as 90 or 180 degree rotations can be directly computed with the same overhead.

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