For the purposes of this question, a polyhedron has triangular facets.
Convex polyhedra are rigid by Cauchy’s theorem. Steffen’s polyhedron is an example of a non-convex polyhedron that is flexible (i.e., non-rigid). However, it appears to have edges of different lengths. My question: are there equilateral flexible polyhedra or are all equilateral polyhedra rigid?
Motivation: I have a bars-and-balls magnetic construction set and I would like to build a flexible polyhedron. But all the bars I have are equal in length.