An unfortunate aspect of all this, is how few good implementations of these algorithms exist outside of big commercial GIS packages. I'm extremely grateful that a public university financed this particular research originally, or we might not have gotten a well funded open source library.
I have been writing a blog post that elaborates on the specification of what I believe is the state of the art DGGS for most applications. It is a specification of the best DGGS I know how to design. This is not proprietary IP, just esoteric knowledge. Will be pushed sometime over the next few
If you look closely, I am one of the authors of the standards for such systems. :) There is a boundary where cartographic systems and technology cease to be useful.
One of the big advantages of the 3D embedding DGGS is that the math is dead simple compared to the forced 2D versions. They are extremely powerful in terms of expressiveness, performance, and precision but also relatively transparent. The mere fact of attacking the 2D problem in 3-space reduces its complexity. People just aren’t used to it. The implicit dimensional reduction of 2-space has consequences. In a few years I think all geospatial data will be handled this way.
Reasons for going to 4D are numerous and varied, such as symplectic geometry only works in even dimensions, image/video reconstruction, matrix multiplication, transformations, and other reasons related to computer vision, gauge theory, and topology.