Axonometric projections together with corresponding graphs for tetra-hexa-cellequator
fullerenes are constructed in the range from 48 to 72. A unified approach for drawing
axonometric projections of the fullerenes was used. The process of 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. As a result, there arises a new atomic configuration and there
is mass increase of two carbon atoms. We obtained direct descendents of the fifth branch of
tetra-hexa-cell-equator family which begins with C48; namely C50, C52,
C54, C56, C58, C60, C62,
C64, C66, C68, C70, and C72.
Among them only three fullerenes, C48, C60 and C72 are highly
symmetric. The symmetry can be easily discovered looking at their graphs. On the basis of
this study, as well as previous investigations the periodic system of fullerenes is suggested.
Keywords: carbon dimer, fullerene, graph, modeling, structure.
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