Schoenhardt Polyhedron

Original creator description

This unassuming shape, the Schoenhardt polyhedron , is actually quite special; it is the simplest non-convex polyhedron that untetrahedralizable (in other words, it cannot be built out of any number of tetrahedra). It has no internal diagonals; every vertex is connected to four others by edges, and the diagonal to the last vertex crosses the valley between two of the sides. I ran into a discussion of this shape and found it difficult to visualize, even with animated versions like the one on the Geometry Junkyard site, so I decided to print a copy. The coordinates in the OpenSCAD script are taken from the POV-Ray file that was animated in the example. This hosted file keeps creator credit and license details.