Constructing flexible polyhedra by twinning

Polyhedra are generically rigid, but can be made to flex under certain symmetry conditions. We generalise Raoul Bricard’s 1897 method for making flexible octahedra to construct an infinite family of flexible polyhedra with self-intersections. Removing an edge from any of these models gives a crinkle, and these can be used to create flexible polyhedra without self-interesection. We show this in a particular example, giving a flexible embedded polyhedron with a large range of motion. We also discuss a novel crinkle.