ccp (continued)

Another imaging of 'close packed cubic', or "face centered cubic", as it is also called, is this:

You start with a layer, that is not closepacked, but rather the conventional rectangular. The second and third layers are dislocated as shown in the picture. It may be hard to see, but each point has 12 neighbours or "ligands". The coordinating polyhedron is a cuboctahedron, which is not "regular". In the simple cubic system each point has 8 ligands, and the octahedron is the coordinating figure. Suppose we are talking about integers! But if we talk about "real" numbers, a paradox will reveal.
I have a cube of points (a;b:c). a b c belongs to the set of real numbers in a certain interval. If I dislocate the layers like said above, and hence changing the structure from simple cubic to face centered cubic, the volume of the cube must decrease. Is there anyone out there who can explain this? The best would be, if you catch me with having made a logical mistake.
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I did a mistake. Hope you see it, too.