semirígididity

Semirigidity is a geometric property of a polyhedron that has been studied in the context of rigidity theory. It was first introduced by Mario Mengucci and Jose Fernando Morales Ramirez in 2014 as a way to describe the behavior of polyhedra that are almost rigid.

A polyhedron is said to be semirigid if it has a non-trivial automorphism group that acts transitively on its vertices, which means that the polyhedron has a symmetry group that contains a non-trivial element that moves every vertex of the polyhedron to every other vertex. In other words, the polyhedron can be transformed into itself in a way that maps every vertex to every other vertex, but this transformation cannot be achieved by a rigid motion of the polyhedron.

Semirigidity is a weaker form of rigidity, and it does not imply that the polyhedron remains rigid under all deformations. However, it does imply that the polyhedron cannot be deformed into a non-convex shape, as this would contradict the assumption that it is semirigid.

Semirigid polyhedra are of particular interest in geometry and topology, as they exhibit a form of rigidity that is weaker than complete rigidity. The study of semirigid polyhedra has led to a deeper understanding of the geometry and topology of these objects, and has also raised questions about the nature of rigidity and its relation to symmetry.

While the study of semirigid polyhedra is still a relatively new area of research, it has already produced some surprising results and insights, and is likely to continue to be an active area of investigation in the years to come.