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Nov 3, 2011 at 20:40 comment added James Cruickshank Thank you for the Maple code (a lot of work if you didnlt already have it!) and reference. I guess I will need to think about this some more. The so called Henneberg conjecture (perhaps authors other than GSS name it differently) seems to be deceptively simple. It is surprising to me (a novice admitedly in this area) that this question has remained open for so long.
Nov 3, 2011 at 20:34 vote accept James Cruickshank
Nov 3, 2011 at 19:33 comment added j.c. Regarding question 1, you may find this 2005 survey "On the Rank Function of the 3-Dimensional Rigidity Matroid" by Jackson and Jordán helpful: cs.elte.hu/egres/tr/egres-05-09.pdf They use different notation but I think that what GSS call the Henneberg conjecture in their book is Conjecture 2.7.
Nov 3, 2011 at 19:23 history answered j.c. CC BY-SA 3.0