Axonometric projections together with corresponding graphs for fullerenes are constructed in the range from 24 to 48. The growth of fullerenes is studied on the basis of the mechanism, according to which a carbon dimer embeds in a hexagon of an initial fullerene. This leads to stretching and breaking the covalent bonds which are parallel to arising tensile forces. In this case, instead of the hexagon adjoining two pentagons, one obtains two adjacent pentagons adjoining two hexagons. As a result, there arises a new atomic configuration and there is mass increase of two carbon atoms. We considered direct descendents of fullerene C24; namely, C2n, where n = 13 – 24.