A method for determining the Avogadro constant using samples of polygraphene made up of multiple layers of graphene is studied. The properties, and methods of producing, monitoring the crystal lattice quality, and determining the geometric parameters of the new materials, graphene and polygraphene, are examined. The method proposed by Fraundorf for creating fractional units of mass and amounts of the material with the aid of a polygraphene hexahedron is modified. The precision of the polygraphene prism technique is found to be low, and a method for determining the Avogadro constant using a sample of highly oriented pyrolitic graphite with a high degree of chemical and isotopic purity offers more promise.Work is currently under way to renew the definitions of four of the SI base units (the kilogram, mole, ampere, and kelvin), which must be accepted at the General Conference on Weights and Measures (CGPM) in 2018, and to develop methods for realizing these definitions. The new definitions will be based on fixed values of the fundamental constants of physics (FCP) [1][2][3][4][5][6]. This approach leads, first of all, to a refutation of the existing kilogram artifact (the international prototype kilogram) and will aid in increasing the accuracy, stability, and reproducibility of measurements using the units of the revised SI in any place at any time. The reference methods for realizing the chosen definitions will play a fundamental role in using the new definitions. This realization of the SI units will be independent of factors related to the effect of natural conditions and human activity, since it will be based on exact values of the FCP, i.e., on natural invariants.There are two major methods for realizing the new definition of the kilogram: silicon spheres and watt balances. The values of the Avogadro and Planck constants determined by these methods diverge by more than 3σ. In addition, the relative standard uncertainty of 2·10 -8 recommended by the International Committee on Weights and Measures (CIPM) has not been attained when these methods are used.This article examines the properties of a promising new material, graphene, which can be used for measuring the Avogadro constant and for creating a new fractional unit of mass on this basis. The methods of producing graphene, monitoring the crystal lattice quality, and determining its geometric parameters are discussed. The method proposed by Fraundorf for creating fractional units of mass and amounts of a material using a polygraphene hexahedron is modified, and its accuracy is estimated [7]. The precision of the graphene prism method is found to be low, at a level of 10 2 -10 3 . A determination of the Avogadro constant using a sample of highly oriented pyrolitic graphite (HOPG) with a high degree of chemical and isotopic purity is more promising. The method based on HOPG can be used to create fractional units of mass and of the amount of a substance within the framework of the revised SI.Properties of Graphene -a Two-Dimensional Allotropic Form of Carbon. Car...