Carbon is the center piece of the elements because it represents the most complete and recurring geometric shape in the form of an icosahedron!
Carbon is the first element that has precisely this shape, It is made up of 12 protons in a icosahedron shape. The 20 trinagular durface area's are where the electrons are positioned. The precise spreading of what triangular surface is occupied when by inner or outer electrons is a separate topic in this model.
Carbon has the valence value (usually) of -4 / +4. Carbon as a nuclet however has normally a +2 / +4 value. The elements in the Carbon group have this shared, nml active carbon nuclet ending.
Carbon at this stage is still un-distorted..... When the first Icosahedron has the next neutron connection added to it (Nitrogen) and reaching a total of 14 protons, an opening is forced on the carbon atom becoming dual in nature by having 2 specific points / area's where the next integrated icosahedron can grow on to.
The gap is a distortion in the icosahedron shape and one would argue that this therefore is erroneous. However, as so often is the case, what appears to be an error, is actually the next step to understanding to a higher degree!
It turns out that the distorted icosahedron is actually supported by 2 times 7 perfect integrated tetrahedrons (in the case of Neon). Nitorgen, Oxygen and Fluorine are half way this next complete shape.
Neon is special in the sense that not the proton strucuture the icosahedron, but the dodecahedron made by the electrons is now perfect. It has the 20 trinagular surface area's completely occupied by inner and outer electrons. This renders the entire nucleus neutralized and shields of the enitre atom from its environment, because there are no more connection points left, the element Neon has beceome inert, that what we call a noble gas!
Chemistry is essentially the same principle, by combining elements that do not have the noble gas configuration are still showing charge differences on the nucleus and will react together and therefore annihilation those charged spots. Now through chemistry, the atoms mimic the noble gas configuration.