A Schönhardt polyhedron is a non-convex polyhedron, chiral, with no interior diagonals, and that cannot be triangulated. See Wikipedia entry for more details: https://en.wikipedia.org/wiki/Sch%C3%B6nhardt_polyhedron

This was designed in OpenSCAD using linear_extrude and 1 line of code! Unsuspected simple, right?!

linear_extrude(height=60,slices=1,twist=150,$fn=1) circle(20,$fn=3);

Happy hacking!