The symmetry operator for a twofold rotation axis parallel to X and passing through the point (x,1/4,1/4) is given by x,1/2-y,1/2-z. To understand this, note the following points: (a) the x coordinate remains unchanged after the rotation; but (b) the y and z coordinates change sign; and finally (c) the origin offset doubles in value when incorporated into the symmetry operator, i.e. 1/4 becomes 1/2.

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