flexible polyhedrons

[Beune]

hello, how may I check whether a polyhedron is flexible?

[geroldsh]

What do you mean by "flexible"? There are only five possible shapes for a regular polyhedron:regular tetrahedron, cube, octahedron, dodecahedron and icosahedron.

check out www.mathwords.com

If you can find a copy of the September/October 2000 issue of Quantum
magazine you will find the article "Flexible Polyhedral Surfaces
by V. A. Alexandrov
Do closed, flexible polyhedrons (without self-intersections) exist?"

[Beune]

I don't know if I am going to give a good definition of a flexible polyhedron, it is a polyhedron (with an inside and an outside, and its faces are parts of a plan), and it can move, but without any evolution on its faces. I don't know if it is perfectly clear, because I don't speak english very well . The movement must be continuous. Some do exist, but they are rare, there is even one that is only infinitesimally flexible, it is called a shaking polyhedron. Thank you for the article.

[Beune]

You can see 2 of them on http://perso.wanadoo.fr/jean-paul.davalan/geom/poly/
(sorry the site is in french)