Hi Alex - you can only turn on control points for a solid if all the faces making up the solids have their "underlying surfaces" with matching control points along their shared edges.
If you have faces that are made up of trimmed surfaces where the "underlying surface" of the face is larger than the visible face boundary and there are trim curves on it cutting off a portion of it, that type of structure won't be able to have control points turned on for it while it is still joined together. You can use Edit > Separate on such an object to break it into individual separate surfaces though, and then turn on control points for those surfaces.
There is some more detailed explanation on this on this FAQ answer here:
http://moi3d.com/wiki/FAQ#Q:_Why_does_show_points_work_for_some_objects_but_not_others.3F
- Michale
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