The Bucky Ball or Spherical Truncated Icosahedron resembles a soccer ball. When I think of the best shape for a three dimension model for Earth's thermodynamic system, that is the cat's ass. Hermann Harde used the shape for a model to determine the surface sensitivity to a doubling of CO2. He had a good idea, just didn't go far enough with it.
The only way to get a true feel for the complex interactions of environmental boundary layers is with a multilayer model. Two layers is just a drop in the bucket which is where Hermann's first shot ended. Because he only used two layers, his estimates appears to be a little on the low side, not that his number is wrong for just CO2, but it is not indicative of the overall system response to CO2.
For outgoing longwave radiation, a minimum of three layers should be required to just get in the ballpark. Using the surface as the reference, the tropopause average pressure and the average surface radiant layer, approximately 600mb, would be need to trace variations in forcing.
Using the Bucky Ball model, the surface would be Bucky sphere with radius equalt to the Earth's average radius, the tropopause a Bucky sphere with radius of the Earth plus the average height of the tropopause and the same for the 600mb boundary layer. With the truncated surfaces aligned, each facet would represent an energy surface analogous to the multi-disc model.
I am not particularly sure why this is confusing to some that have heard my suggestion. It is a simple three dimensional model that could standardized the information used for various approaches to predicting climate fluctuations. When it comes to CO2 forcing, standardization is sorely needed since most folks I know don't live in the tropopause. It is the impact at the surface that matters, in any case.