In the biography "King of infinite space: Donald Coxeter, the man who saved geometry" by Siobhan Roberts, the following passage describes an aspect of the subject's relationship with Buckminster Fuller:
Coxeter was not the first to be frustrated by Fuller. Fuller was neither an architect nor engineer nor mathematician by training, and he became a controversial figure among experts in all those fields. He made awkward geometric mistakes, such as how many spokes are needed on a wheel to hold it rigid (Fuller said twelve instead of seven).
I was intrigued by the claim that seven spokes are needed on a wheel to hold it rigid. Searching Google does reveal that Fuller seems to have thought the answer was twelve, but I cannot find any other claim that it should be seven.
I cannot figure out a (mathematical) model in which seven spokes is the answer (nor twelve, for what it's worth). It certainly seems that the spokes are assumed to be "tension" only, as of course there are three-spoke bicycle wheels made of solid (rigid) spokes. In other words, I assume the subject under discussion is wire wheels, where the spokes "function mechanically the same as tensioned flexible wires".
I have constructed a few models, definitely unrealistic, where the minimal number of spokes is three. Can anyone give a mathematical model of tension-spoked wheels where the minimum number of spokes is seven (or twelve, or perhaps any finite number greater than three)?
[The "inverse problem" in the title refers to the fact that in this situation, we know the answer but not the question!]