If an object is at point x,y,z (Cartesian coordinates) and its symmetry mate is related by...

If an object is at point x,y,z (Cartesian coordinates) and its symmetry mate is related by a 21 screw axis, what is the location in Cartesian coordinates for the symmetry mate?

Expert Solution

Hello!!

A screw axis is a symmetry operation in which rotation is followed by translation i.e. you first rotate the object by an angle and then translate it in a perpendicular direction by a distance 1/a. Assume the screw axis to be n_a axis, then here, = 360/n and the translation is to be made in the perpendicular direction by 1/a. You can consider it to be absolutely similar to a screw (hence getting its name).

Here, for 2₁ screw axis, the object has to be rotated by an angle of 360/2= 180^o followed by a translation of 1/2.

Thus, in your case, for a 2₁ screw axis, if we consider c-axis as our axis of rotation, the object will change its coordinates from (x,y,z) to (-x,-y,z) upon a 180^o rotation because for 180^o rotation, the cartesian coordinates remains the same for the direction of the axis and they are inverted for the other 2-axis. This will further be followed by a translation of 1/2 along c-axis.

Finally,

Feel free to ask any of your queries in the comments.

queen_honey_blossom answered 4 months ago

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