The nuclear geometry has been developed by analogy with the fullerene geometry. On the base of this geometric approach, the structure of carbon isomers and isotopes, which can be obtained by means of nuclear synthesis, has been designed. The mechanisms of possible nuclear reaction are discussed. Carbon is an unusual element. It has four isomers of different symmetry: three-fold, six-fold and tetrahedral ones, two being stable and one halfstable. The isotopes of carbon inherit the structure of the isomers.