Birosettes are model flexors (Q2417349)

The notion of model flexors was introduced by the second author in several articles as an analog of theoretical exors. There are only several known examples of theoretical flexors, including the Bricard octahedra and Connelly and Steffen exors [\textit{R. Connelly}, Publ. Math., Inst. Hautes Étud. Sci. 47, 333--338 (1977; Zbl 0375.53034); \textit{P. R. Cromwell}, Polyhedra. Paperback ed. Cambridge: Cambridge University Press (1999; Zbl 0926.52014)]. In practice, there exist polyhedra which are not theoretical flexors, i.e., admit considerable deformations without usual changes in the shapes and sizes of faces but with variations of dihedral angles. These polyhedra were called model flexors. In the second author's articles the main attention was given to special polyhedra (Alexandrov-Vladimirova starlike bipyramids). Their model exibility was established by the second author using the notion of linear bending. The phenomenon of model exibility was actually discovered by the second author not for starlike bipyramids but for a Jessen orthogonal icosahedron also known as a Douady shaddock [\textit{M. Berger}, Géométrie. Vol. 5: La sphère pour elle-meme, géométrie hyperbolique l'espace des sphères. Paris: Cedic/Fernand Nathan (1977; Zbl 0423.51003)]. In this article, the authors study one more class of model flexors whose structure was proposed by the second author. These polyhedra are called birosettes. Their geometric features are analyzed and their model exibility is explained. In particular, they also consider special infinitesimal bendings of birosettes. They prove that, in the family of all birosettes, the nontrivial infinitesimal bendings of first order with the indicated properties are admitted (solely) by the extreme birosettes. They also construct physical models of birosettes for small values of \(n\) (every birosette contains two faces congruent to a regular \(n\)-gon) and supplement them with computer and graphic experiments.