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Question

ABABAB layering pattern is called hexagonal close packing, found in HCP lattice.
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Solution

Hexagonal close-packed (hcp) has ABABABA (every other layer is the same) arrangement. In this arrangements, each sphere has twelve neighbors. For every sphere, there is one gap surrounded by six spheres (octahedral) and two smaller gaps surrounded by four spheres (tetrahedral). Relative to a reference layer with positioning A is overlapped by layer B. Every sequence of A and B without immediate repetition of the same one is possible where every other layer is the same and gives an equally dense packing for spheres of a given radius.

418288_264427_ans_2d1706f74cb94d0f9bd2437d147c0ec1.png

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