
net by Peter R. Cromwell 
The LiveGraphics3D applet has some difficulties to well display faces which are almost coplanar. 
Two important results concerning the flexible polyhedra:
• A convex polyhedron is rigid. (Cauchy's rigidity theorem, 1813)
• During the deformation of a flexible polyhedron its volume remains constant. (bellow's conjecture, ConnellySabitovWalz, 1997)
• Bricard's octahedra (1897): assemblings of two "square pyramids", they have intersecting faces and thus can only be realized as articulated structures (Raoul Bricard was a French engineer).
• Robert Connelly's "sphere" (1978) uses the Bricard's idea to avoid intersecting faces (a model simplified by Kuiper and Deligne has 18 faces and 11 vertices).
• Jessen's orthogonal icosahedron is infinitesimally flexible (shaky polyhedron)
references: 
• Rigidity of Polyhedra web pages (McGill University  Montréal, illustrated by J.Shum)
• Les polyèdres flexibles et la conjecture du soufflet by Thierry Lambre (bulletin 471 APMEP, page 533, in French) • Polyhedra by Peter R. Cromwell (Cambridge University Press  1997, pages 239246) • Steffen's polyhedron on MathWorld and on mathematik.com 
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convex polyhedra  non convex polyhedra  interesting polyhedra  related subjects  October 2007 updated 27102007 