The axis is a axis through the centers of opposite cube faces: a half turn permutes atoms within each species. A body diagonal through sites 1 and 8 is a axis: a third turn fixes those two opposite vertices and cycles the other three vertices of each tetrahedral sublattice. These are symmetry operations of the tetrahedral symmetry group ; a quarter turn about would interchange the two chemical species and is not a symmetry of the specified cluster.

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