Aligning 3D objects in Blender

I've been learning how to use Blender and working on some polyhedral compositions. One issue that comes up is aligning polyhedra precisely face to face. This is the case that the internal snapping function seems to not be able to handle (although maybe I am missing something there). I have tried two different alignment add-ons with some success: Align by faces and Precise Align. While Align by faces is very simple in use it is not quite clear to me why sometimes it works and sometimes doesn't. Precise Align is more difficult to set up and it took me some time to figure out how to get the axes right, but in the end it can be made to work more predictably. I've also used the Add Solids plugin for adding extra mesh objects like the dodecahedra in this example.

Here is what Align by faces do:
1. Select a face on each object in the Edit mode.

 2. In the Object mode, select both objects and call the plugin by pressing the Space bar.

 3. Et voilà, aligned.

However, this doesn't always work. Depending on the rotation of your two objects with respect to each other and on the faces you choose about half the time they do not precisely line up by rotation.

Case in point:
1. The same face has been selected on the left object as above.

2. But a different face is selected on the right object.

 3. The result is that they are lined up along a plane but not vertex to vertex.

 So, it takes some guesswork to pick two faces that will line up perfectly. Since my objects are symmetrical I have a lot of planes to choose from. If the objects are asymmetric and the faces that I want to line up are not in the same, parallel, or symmetric plane (at least I think this is what's going on here) then they won't line up perfectly, missing each other by a rotation. And this is the case in which Precise Align works.