Graphene, Carbon nanoribbons, Carbon nanotubes and Fullerene (Buckyball) are allotropes of carbon which are widely used in Nanotechnology research due to their remarkable properties. Electrical and mechanical properties of those allotropes vary with their molecular geometry. Theoretically, an infinite number of such geometries do exist and it is impossible to physically prepare samples of all of them in the real world. This paper is based on modeling the atomic structures of those carbon allotropes with all the molecular geometries in 3D space, given variable user inputs to select the geometry, and customizing the view varying the angle and colours. Equations to derive the coordinates of the atoms, algorithms to derive the orientation of the bonds of the molecular structures and the manner in which the algorithms are implemented using java3D are described in this paper. Successful results were obtained after the implementation of the algorithms which are illustrated with few screenshots at the end.