Large-scale production of perfect conical carbon nanostructures that are fundamentally different from the other nanocarbon materials, such as buckyballs and nanotubes, can be made using the so-called Kvaerner Carbon Black & Hydrogen Process. This involves pyrolysis of hydrocarbons using a torch plasma process. The carbon cones that occur appear in five distinctly different forms. In addition, disk-shaped particles may be produced. Here we report about the current status for the experimental research and theoretical modeling of these particles, which have properties different from the other known forms of carbon.