Steffen's polyhedron

In geometry, Steffen's polyhedron is a flexible polyhedron discovered (in 1978[1]) by and named after Klaus Steffen [de].

[2] It has nine vertices, 21 edges, and 14 triangular faces.

[3] Its faces can be decomposed into three subsets: two six-triangle-patches from a Bricard octahedron, and two more triangles (the central two triangles of the net shown in the illustration) that link these patches together.

[4] It obeys the strong bellows conjecture, meaning that (like the Bricard octahedron on which it is based) its Dehn invariant stays constant as it flexes.

[5] Although it has been claimed to be the simplest possible flexible polyhedron without self-crossings,[3] a 2024 preprint by Gallet et al. claims to construct a simpler non-self-crossing flexible polyhedron with only eight vertices.