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I've been recently reading the very clear text of Burns and Glazer entitled

*Space Groups for Solid State Scientists*in the context of my thesis which requires understanding of symmetries of crystals, more specifically symmetries of (approximate triply periodic minimal surfaces) ATPMSs.

Currently I am stuck at a point on the symmetries of diamond unit cells, and their ATPMS counterparts are defined. These structures are classified to be under m \bar{3} m, which seem to be involving four fold rotational symmetries along the normals of the cell surfaces as well as centrosymmetry. But neither the diamond crystal nor its ATPMS version encapsulates these symmetries, at least to my understanding.

What am I missing here? Thank you very much for the comments.

Kumar