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Arranging spheres ABABAB type in 2D gives us close packing. Now, this layer if arranged in ABABAB (in 3D) gives us HCP and if arranged in ABCABC (in 3D) gives us FCC.

What do we get if we arrange it in AAAAA type (in 3D)? (we are talking about one type of spheres only)

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The question is a little confusing, so I will interpret your 'ABABAB' type in 2D to mean a simple hexagonal layer (so, the same layer as used for your hcp and fcc packing). So, a stacking of a simple hexagonal layer, each layer directly above the other, will give a structure looking like right hexagonal prisms - or right triangular prisms if you look a bit more carefully.

Anyway, the resulting structure is the simple hexagonal Bravais lattice with a single atom basis. Hcp is also a simple hexagonal Bravais lattice, but with a two atom basis, one each from plane A and plane B. I do not know of any elements that crystallize in this crystal structure (but am open to corrections!).

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  • $\begingroup$ You have interpreted it in the right way. I see that in both the cases (using the simple hexagonal 2D layer in ABAB and AAAA way in 3D) we are getting the same simple hexagonal bravais lattice. But, the atomic arrangement is totally different in both. In chemistry books simple hexagonal bravais lattice is always means ABAB type. Nobody talks about AAAA. Maybe, it is because it does not exist in nature. Whatever, thanks for the answer. $\endgroup$
    – ravi
    May 13, 2015 at 3:25
  • $\begingroup$ No, the atomic arrangement is not totally different - the underlying Bravais lattice is the simple hexagonal lattice. The unit cell that sits on that lattice is different, leading to a different point group. As for it existing in nature, it is true that I can't find an element that crystallizes in simple hexagonal, but I suspect a good synthetic chemist could come up with a unit cell likely to result in simple hexagonal... $\endgroup$
    – Jon Custer
    May 13, 2015 at 13:26

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