Fejes-Toth and Heppes
had presented this example
(partially disassembled) of 12 tetrahedra in 1963. No tetrahedron can
even be wiggled without disturbing the others. (Although a group of
three can be translated away.)
Already in 1954, de Brijn knew that any set of convex objects could be
exploded:
taken apart with one hand per object.