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In this recent question Math puzzles for dinner 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?

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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. Also see "Review of Form-Finding Methods for Tensegrity Structures" and the MS thesis Kinematic Analysis of Tensegrity Structures.

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    $\begingroup$ Many pictures of such objects can be found on google images google.com/images?q=tensegrity%20prism $\endgroup$
    – j.c.
    Commented Jun 26, 2010 at 13:07
  • $\begingroup$ oh I did think it was my creation. ar... well let's say I'm glad that my puzzle became so popular so quickly ;-) $\endgroup$
    – Pietro Majer
    Commented Jun 26, 2010 at 18:17

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