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[The problem is roughly] Toy “Supermag” makes it possible to construct, among others, polyhedrons — e.g. tetrahedrons, cubes, and many irregular polyhedrons, where the edges of the polyhedron are made of magnetic bars, which are connected at the vertices with the help of steel balls. The steel balls fix the endpoint of a steel bar to itself firmly, but the angle between magnetic bars meeting at a steel ball can be changed with a little effort. It appears that a tetrahedron is a rigid construction, but a cube can be easily deformed. Prove the following theorem: a convex polyhedron is rigid then and only then if all the faces of the polyhedron are triangle?

In the problem source hint was somewhat by use of Euler formula on polyhedron and concept of degree of freedom.

How to solve the problem ?

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  • $\begingroup$ any sort of way of approach to the problem may help $\endgroup$ – Bijayan Ray Jan 2 '19 at 13:11
  • $\begingroup$ the converse statement find solution if it can be proved that degree of freedom exceed 6 in such a case $\endgroup$ – Bijayan Ray Jan 2 '19 at 13:14

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