Tim claims seven is minimal, echoing claims in a new biography of H.S.M. Coxeter, the late master geometer, to whom Bucky dedicated his two volume magnum opus.
The question is important in part because the bicycle wheel marks a transition from compression-heavy designs to lighter weight tension-based solutions.
The hub in a traditional wooden spoked wheel "pole vaults along" (Bucky's imagery), its spokes pushing downward against the rim, whereas the bicycle wheel's hub hangs from above, reaching out to the sides to prevent the rim from buckling outward.
For Fuller, learning to design around tension was a critical "more with less" strategy that would help humans aboard Spaceship Earth take better care of themselves over the long haul.
I've weighed in on the side of empiricism in this thread, plus hinted at other mistakes we may find in Synergetics, even beyond those already listed, by Robert Gray and others.
My friend Tom Ace shares a lot of Tyler's skepticism regarding Synergetics, plus knows a lot about bicycle wheels. More empirical testing is a good idea. [link]This book, first published by Macmillan and now on the web, should not be considered the last word in the discipline, nor even a last stand, but a promising beginning, a trailblazing exploration.
Yet how many school kids even know there's a legacy, a "geometry of thinking" to explore? And who was this Coxeter guy and what means "tensegrity"?
No child should be left behind when it comes to accessing their own best heritage, American or otherwise. As I've written on Synergeo recently, a Yahoo! eGroup:
For my part, I want to recruit more high powered players who will help me get at least the basics, the concentric hierarchy and its ball packing context, televized and more evenly distributed, so it becomes a part of the background noise of our culture.Fortunately, I'm seeing signs that we're turning this corner and really starting to get the word out to our kids.
Once synergetics is more overtly in the background, I'll make less noise in the foreground and probably come off as less combative and competitive to boot. [link]
So perhaps our esoteric little arguments will gain wider currency, and even this little bicycle wheel question may help us recruit future scientists.