The high hydrogen capacity of carbon nanomaterials has stimulated hydrogeninvestigators to concentrate much attention not only to their hydrogen capacity, but also to the peculiarities of the course of hydrogenation process and to the behavior of fullerene molecule in different aggregative states. The experimental study of peculiarities of fullerene C-60 existence in three aggregate states has been conducted in this paper. We have studied the features of the formation and behavior of C-60 molecules in the gaseous phase and in solutions. It has been shown that the fullerene molecule, as three-dimensional spherical polymer, consists of pentatomic molecules, has its own sp(x) - hybridization and, for this reason, fullerene should be considered as a new allotropic modification of carbon. We have escertained that at temperatures above 250 IC the fullerene molecules in solutions exist in two states - beta and gamma. In this case the dualism of fullerene molecule permits to form the colloidal solutions in the gamma-state. We have shown that crystallization of fullerene in three different forms is a consequence of its existence in the form of three stable isomers. The spatial diagram of carbon allotropic modifications at two levels of organization (gaseous and crystalline) has been proposed in this paper. Copyright (C) 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.