In this recent question [Math puzzles for dinner](https://mathoverflow.net/questions/29323/math-puzzles-for-dinner/29343#29343) we had a nice time as we were asked to provide new maths puzzles for dinners. I suggested the following:



> 
> Given three equal sticks, and some
>  thread, is it possible to make a rigid
>  object in such a way that the three
>  sticks do not touch each other? (all
>  objects are 1 dimensional; sticks are
>  straight and rigid, and the thread is
>  inestensible).
> 
> 
> 


I'm not particularly fond of maths puzzles, and I found this one in order to satisfy the party in a dinner of non-mathematic people, when I'm asked for a puzzle. Indeed, it's suitable for a dinner, and people get to the right conclusion in reasonable time, amusing themselves and disputing a bit. 


Possibly as a consequence of the fact that I always proposed it to non-mathematicians, who are not interested in the proof, now I realized that I do not have, or I forget, the proof for the answer (a bit embarassing indeed). Can somebody find a quick proof for the answer, without too many technical computations?



Sticks and thread
Instead of a proof, I will provide references. It's called a "tensegrity prism". See especially sections 1.4, 3.5 and 3.6 of [*Dynamics and Control of Tensegrity Systems*](http://books.google.com/books?id=LxItccmYhBkC). Also see ["Review of Form-Finding Methods for Tensegrity Structures"](http://www-civ.eng.cam.ac.uk/dsl/publications/tensegrity.pdf) and the MS thesis [*Kinematic Analysis of Tensegrity Structures*](http://scholar.lib.vt.edu/theses/available/etd-12022002-155829/).


