[math-fun] How many spokes does a bicycle need?

In the biography of H.S.M. Coxeter "King of Infinite Space", one section describes his interaction with Buckminster Fuller. It states that Fuller erroneously claimed that a bicycle wheel needs 12 spokes "to hold it rigid", whereas the correct number is 7. This seems to be stated as a fact of geometry, rather than one of structural engineering. Anybody have any insight into this claim? --Dan P.S. In case anyone's interested, this is the only biography of Coxeter I know of and it's filled with interesting facts about his life. But it is sadly lacking in details about his mathematical accomplishments, other than in the vaguest terms. Those who sleep faster are more rested sooner.