Classification and Nomenclature of Planets in the Mass-Radius Plane

6500+ exoplanets have been detected using various techniques. This prompted the emergence of many recent works on the taxonomy, or classification, of exoplanets. However, there is still no basic, fundamental definition of 'What is a planet?'. IAU has forwarded a definition in 2006, which however, raised more questions than it solved. The first task here is to establish if there are limits on the size/mass of planets. The lower mass limit may be assumed as of Mimas (0.03 EU) - approximately minimum mass required to attain a nearly spherical hydrostatic equilibrium shape. The upper mass limit may be easier - there is a natural lower limit to what constitutes a star: 0.08 SU. But then there are brown dwarfs: IAU has defined brown dwarfs as objects exceeding the deuterium burning limit (~13 JU), and giant exoplanets generally have masses of 0.3 to 60 JU. The resolution requires assembling the basic physical parameters that define planets quantitatively. Mass and radius are the two fundamental properties, and we propose to use a third correlated parameter: the moment of inertia. Based on this, we create the parametric Fundamental Planetary Plane where the two parameters are correlated with the third. The fundamental planetary plane (FPP) with turn-off point diagrams is constructed for visual representation. We propose an alternate potential description of a planet definition as 'A celestial spherical object, bound to a star or unbound, that lies on the fundamental planetary plane, within a mass range between 0.02 EU to 13 JU'. This definition is intended to complement existing taxonomies by providing a quantitative, structure-based criterion applicable to both Solar System planets, exoplanets and free-floating planets. These turn-off point diagrams serve as an alternative to the Hertzsprung-Russell (HR) diagram, but for planets.