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Symmetrical Twist Assignment, a chimera

A corner cubie may be moved to any of the eight corner cubicles in three different ways; untwisted, with clockwise twist or with counterclockwise twist. The standard convention is to assign the twist with reference the orientation of the cubie's U/D facelet vis-a-vis the cubicle's U/D face. If the cubie's U/D facelet is on the cubicle's U/D face the cubie is untwisted. If the cubie's U/D facelet is rotated 120° clockwise from the cubicle's U/D face the cubie has clockwise twist and vice versa. The disturbing thing about this convention is that it is unsymmetrical. Under this definition the 12 q-turns have different effects on the twist of the cubies turned. Turns of the U and D faces have no effect on the twist of the cubies while a q-turn of any of the other four faces twist two cubies clockwise and two cubies counterclockwise. Since all the faces are symmetry equivalent it has always seemed to me that there ought to be a way of defining corner cubie orientation which preserves this equivalence.