Center of inversion of cubic diamond structure?

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SUMMARY

The center of inversion for the cubic diamond structure is not located at the coordinates (2,2,2) as initially thought. Instead, it is determined to be at the midpoint between two atoms, specifically at (2.5, 1.5, 0.5). This conclusion arises from the analysis of the positions of the atoms within the cubic lattice, which reveals that the points (1,1,3), (3,3,3), (1,3,1), and (3,1,1) do not exhibit centrosymmetry about the point (2,2,2).

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I'm having hard time finding the center of inversion of cubic diamond structure.

upload_2018-11-20_17-53-41.png


At first I thought (2,2,2) would be the center of inversion, but (1,1,3), (3,3,3), (1,3,1), (3,1,1) (i.e. four atoms inside the cube) are not centrosymmetric about (2,2,2).
 

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Ah, I see. It's on a midpoint between two atoms like (2.5, 1.5, 0.5)...
 

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