In the above video the planet is made up of 125x125x6 vertices's and the moon from 65x65x6 faces. There is currently no complete LOD functionality. When fully implemented each face recursively subdivides into 4 faces of equal area, resulting in the level of detail of each face increasing by a level of 4 with each divide.
With some clean programming, a vertex should never have to be calculated more than once (unless the player moves a distance away and the section is deleted from memory). The parent will populate each of its children with the relevant subset of its data, and only the unknown sections calculated, resulting in lower memory usage as well as faster run time higher LOD generation.