Upon further modification of the "Solid," it seems like maybe the Object name was limiting the selectability
of the various parts of the solid.
Attached is a modified .3dm, in which the Blue denotes two different edges.
There is an inner surface to the spherical solid, in the shape (more or less) of an elliptical cylinder, with curved top and bottom.





Edit: The former Blend that I was doing was actually with the curvy edge of an extruded ellipse:

Hi Brian, yeah it looks like one of the faces of the solid was hidden which is why it looked somewhat weird.

You can have names and styles and visibility assigned to individual face and edge sub-objects within a solid too like that.

- Michael