Maybe the most unique puzzle which grew out of this discussion is Oskar's Bubble Block. And I'm glad I can say I got to see this puzzle first hand at G4G10. However its geometry still confuses me. It has 4 axes of rotation but I don't know if they all meet at the same point or not. ...
I currently have this puzzle in pieces, haven't yet assembled it completely but looking at the core i can say for sure that all the axes share one origin, all the cuts are at the same depth, and the angels between the axes are different.
I added the varying angels between cuts rule specifically for the Hexagonish Block and the Bubble Block.
What about puzzles with icosahedral symmetry and fairly deep cuts? Those have varying depth and angles, but no offset axes or stored cuts.
I can't really picture what it is that your describing but judging by what your saying no I wouldn't consider this to be boublized.
What about all the Siamese cubes? I think what differentiates the Siamese puzzles from the boublized puzzles is that some (not necessarily all) pieces can be moved from one core (intersection of two or more turning axes) to another.
When you say Siamese cubes what my mind immediately goes to is two puzzles glued together. So I'm going to look at just one of then say that individually they are not boublized. The reason for that being is the stored cut is not caused by any of the three criteria, but instead bandaging.
David Pitcher wrote:
... already have their own self-explanatory names (multiple origins, varying angles between axes, stored cuts, etc.). Given this, I'm inclined to say that despite the incredible creative outpouring that this thread inspired, we don't really have a new phenomenon that needs a new name.
Though I'm hesitant to say so I see were your coming from and think you may be right.
This way both puzzles could be made with the same pieces. It's on my to-do list and I hope to get there in the next few months. One puzzle is ahead of this on my to-do list and I've also got a few puzzles to assemble, break-in, and sticker. Just need more free time.
I'd really like to see this happen
P.S.On 12 April, I am the last speaker at the 2012 Dutch Mathematical Congress. My primary goal is to introduce jumbling and boublizing to professional mathematicians and get at least one student or PhD to start studying these phenomena.
I can't wait to hear how this turns out.