First of all, thanks ever so much for replying to this thread.
I thought the lack of answers was due to the typical "emabrassingly stupid question" effect.
From: Zeno Concord
Searching on "hinge" I got a few relevant articles. Here is perhaps the most useful:
/54/e1/35124/1.htmlApparently hinges are not very reliable, and people are hoping that Havok 2 will help matters. Instead of using hinges, the general technique is to cut the object so that its center coincides with the new edge, and then do the usual rotation.
Unfortunately, you cant get an equilateral triangle of any size doing it that way.
From: Zeno Concord
Seems there ought to be a way of changing the center of rotation by shifting the local center of the object, but I see suggestions that this is not possible either. So you have to do the appropriate translation/rotation/translation in world coordinates.
I tried extending a thin"stick" out from one side of each triangle so that the COG was on the edge but that didn't work. I think the tools might have been changed almost at the same time I was doing that however so I might have been wrong about that.
I think my problem is basically just inexperience with the tools. For instance I think I must have been the last person to know they changed them.

Also "hinge" is a menu selection (if it's the same thing) and I hadn't noticed that or I probably would not have posted the request.
The whole deal with rotations is hazy to me as well as the difference between "world" and "non-world" coordinates, and not for lack of trying to analyse the thing. On the other hand I am sure in a few months I will be amazed at how foolish I was (now) when the solutions are likely obvious.
It was also a great surprise to me the first time I put a grid texture on a block and watched what happened to it when I "clipped" the edge. Who would have thunk that rather than being clipped the block is actually collapsing in on itself? Lots of this stuff is non-obvious to newbies like me.
From: Zeno Concord
Sounds like it will be worthwhile coming up with some building tools that compute the proper translations and rotations for you and move objects into alignment. I will be happy to work with you on that, as I need to understand the very same thing for one of my projects. I'll be looking for you.
Yes. I have found the "ringmaker" and "shapemaker" tools invaluable. Something like that for geometric solids would be a godsend. Unfortunately again, database scripting is about as "codey" as I get so I would not be much help in designing such tools.