Many studies discuss carbon-based materials because of the versatility of carbon elements. Depending on the processing conditions of a carbon precursor, carbon changes state behavior. The electron transfer mechanism occurred to convert carbon from one state to another. In conversion, the dash-shaped energy bits involved transferring electrons to nearby unfilled states. The involved dash-shaped energy has partially conserved behavior. A transferring electron is also under partially conserved forces. Carbon atoms equally evolve and equally develop structures of one dimension, two dimensions, and four dimensions, respectively, when in the graphite, nanotube, and fullerene states. Here, the already associated dash-shaped energy bits bind the carbon atoms. A two-dimensional graphite structure or amorphous carbon structure also forms. The structural formations in diamond, lonsdaleite, and graphene state atoms involve different shaped bits of energy. The bit of energy has a shape like a golf stick. By involving four bits of golf-stick-shaped energy, all four electrons of the outer ring of the depositing diamond state atom undertake an additional clamp of all four energy knots of the outer ring of the deposited diamond state atom. A depositing diamond state atom binds to the deposited diamond state atom from the east-west surface to the south. Growth is from the south to the east-west surface, so the structure of the diamond is a tetra-electron topological structure. The lonsdaleite state atoms bind from the surface east-west to a bit south. However, in glassy carbon, the layers of gaseous, graphite, and lonsdaleite state atoms bind simultaneously. The order of these layers repeats in the growth process of glassy carbon. The carbon-based materials also study Mohs hardness. This study is very different from the previous ones on carbon materials.