My textbook states these ways of stacking 2D layers to make 3D close packed structures:
- Square close packing layer over Square close packing layer (though not written explicitly, the illustration imply stacking done in a non staggering manner), generating Simple primitive cubic unit cell lattice.
- Hexagonal (2D) close packing layer over Hexagonal (2D) close packing layer (here, again not stated explicitly, but the illustrations imply it is done in staggering manner so that one layer just fits right in the depressions of other layer) giving two different close packed structures: hcp and ccp
However, they did not mention the two cases arising naturally (out of curiosity maybe):
a) Square close packing layer over Square close packing layer done so that the second layer fits just right in the depressions of the first layer, i.e. in a staggering manner so the layer pattern is of 'ABAB...' type.
b) Hexagonal close packing layer over Hexagonal close packing layer in a non-staggered manner, which might generate a lattice with the primitive hexagonal unit cell, layer put in the pattern 'AA...' type.
The case (b) was easier to work out its unit cell's type, however I am unable to comprehend the 3D structure of what type of unit cell case (a) can generate.
My question is, are these cases of lattice arrangements possible? If yes, then what are their respective unit cells?