Clever rebranding aside, it's a well known framework in crystallography and architecture: just pack spheres together ala Kepler and you've got it (the CCP, the FCC) on your screen. The underlying computer graphics likely use the well-known 3D matrix libraries, which is not a problem. 3D embeds seamlessly in 4D.
Note that 4D as used above is what today's thinkers'd call a "meme" -- a take-off on "gene" but "of thought" instead of "of DNA" -- meaning it transmits much more quickly, and takes part in a more kinetic and mutable economy, that of language and culture.
In Bucky's youth, 4D had been recently coined and resonated with many thinkers, including Einstein of course, but also P.D. Ouspensky, a Russian, and many cutting edge artists (Linda Dalrymple Henderson has a good book on this). Bucky grabbed onto 4D (the meme) and combined it with architecture: newfangled and futuristic ideas about assembly line housing. Turns out Alexander Graham Bell was into using it as a space frame as well.
In hindsight, the once-volatile 4D meme appears to have settled into three stable compounds:
- In Einstein's domain, it meant 3D plus Time. "Time the fourth dimension" became the pop culture hallmark of relativity, both general and special, and from this meme complex we inherit the lingo of "three spatial dimensions" (before Einstein, you wouldn't need to say "spatial" because "temporal" hadn't been set off as a fourth dimension).
- In Euclid's domain the 3D coordinate system (also known as XYZ) has become extensible to n-dimensions (nD), e.g. you might have a 9D sphere with a center at (0,0,0,0,0,0,0,0,0), and a bunch of other spheres touching it, each with a 9-tuple address of its own. In this meme-pool, 4D does not connote Time. All the dimensions are "space-like" and get the same treatment. The great Canadian geometer H.S.M. Coxeter operated in this domain, the realm of nD Polytopes (e.g. the tesseract or hypercube).
- Fuller's 4D is neither Euclid's nor Einstein's. He went from hanging houses (houses and skyscrapers suspended from central utility masts) to geodesic domes by way of sphere packing investigations, similar to Kepler's in many ways (the rhombic dodecahedron is key). For Bucky, the tetrahedron, with its four faces, became tightly bonded with 4D. The tetrahedron is the simplest cage or container, made from the fewest bars (only six, compared to the cube's 12). Despite all this talk of ants crawling around spheres or donuts, with limited degrees of freedom, we're still thinking in volume. Flatland is unimaginable. Conceptuality is volumetric at its Kantian core. Rather than characterize space as "3D" based on "height, width and breadth," Fuller, ever the contrarian, labeled it "4D" -- because of the tetrahedron's having four corners and four faces. "Height, width and breadth" never really come apart as isolate or atomic, are more codependent than independent.
Signalling you're "4D" still connotes futuristic, high tech, long term, invested in over-the-horizon possibilities. Fuller's meme complex is especially easy to translate into attractive eye candy -- it's been good for that for years. So watch for it, and maybe you'll see what had previously been invisible to you, because you didn't know what to look for.
