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Recitation nine - Recitation eight Question 1 We have seen...

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Recitation eight Question 1 We have seen centered cells in three dimensions (bcc and ffc e.g.) but they also exist in two dimensions. Consider the above wallpaper design on the left . It has both rotational and translational symmetry. 1. Draw the smallest unit cell possible. (Note: the angles between the two unit vectors are not 90 degrees in what is called the primitive cell ) 2. How many left and right crescents are there in a unit cell? 3. Are the two basic unit vectors of the same length? 4. Draw a vertical line around which the pattern is a mirror image of itself 5. Do the same in the horizontal direction 6. What angle do these two mirror lines make with each other? 7. Now construct the smallest unit cell possible that has its unit vectors in the direction of the mirror lines 8. How many left and right crescents are there in this centered cell? 9. Are the unit vectors of the centered cell of the same length?
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