Model flexor

A family of polyhedra possessing unusual, contradictory from mechanics point, deformation properties is found. On one hand, models of these polyhedra admit free continuous large reversible bending without visible distortions of the material. On theother hand, the polyhedra themselves are rigid and do not admit continuous bending inthe sense of the Cauchy definition. In this case the reason for the physical model to beflexible is the existence of mathematical linear bendings of polyhedron. 
 The linearbending of bipyramids qualified in terms of the theory of dynamical systems of V. I. Arnold as a nonrigid, sort or slow, loss of stability is new phenomenon in mechanics of deformable solid bodies. Considered as a two-parametrical dynamic system, the linearbending of a star-like pyramid represents an original geometrical machine ofcatastrophe supplementing the well studied physical models of Ziman and Poston.