and The design of the pin is what I would call a tetrahedron. If that tetrahedron was pushed into a fitting that had three fixed sphere, that would constrain 3 Degrees of Freedom (DOF).
I'm not recommending this design, I'm just providing some food for thought. This configuration has the effect of a soft spring to prevent rotation. The much better design is the tetrahedral pin that goes into a matching tetrahedral pocket as you have shown, and such a configuration is like a very stiff spring to prevent rotation.
For frictionless contact of the three spheres on the three flats, there is no torque to prevent the first increment of rotation, but as the contact point moves along the plane, the flat faces of the pin move their contact point off center and develop a contact force. Consider the case where the other end of the shaft is fixed and the pin is inserted into a 3-sphere pocket that rotates about the shaft axis. Now as the rotation increases, an axial force develops to push the pin out of the 3-sphere pocket.
The axial reaction force as a function of rotation is shown below.