Cutting Along a Symmetric Quadrilateral to Construct an Embedded Flexible Dodecahedron

Abstract Until recently, the simplest known flexible polyhedron embedded in Euclidean three-space was Steffen’s polyhedron on nine vertices. However, in 2024, an embedded flexible polyhedron on eight vertices was discovered. It attains the known lower bound for the number of vertices, showing that the simplest embedded flexible polyhedron has eight vertices. We introduce a method for making new flexible polyhedral surfaces from old ones. This general method applies to the above minimal example, giving another proof of its flexibility. We also construct a different, embedded flexible dodecahedron on eight vertices. This improves both the range of motion and the simplicity of the exposition.