Steffen's polyhedron
In geometry, Steffen's polyhedron is a flexible polyhedron discovered by and named after. It is based on the Bricard octahedron, but unlike the Bricard octahedron its surface does not cross itself. It has nine vertices, 21 edges, and 14 triangular faces. Its faces can be decomposed into three subsets: two six-triangle-patches from a Bricard octahedron, and two more triangles that link these patches together.
It obeys the strong bellows conjecture, meaning that its Dehn invariant stays constant as it flexes.
Although it has been claimed to be the simplest possible flexible polyhedron without self-crossings, a 2024 preprint by Gallet et al. claims to construct a simpler non-self-crossing flexible polyhedron with only eight vertices.