Because I was bored and had waaaaay too much free time on my hands, I decided to take a shot at designing a Tera-Hexaminx. It was successful! Below are some photos.
First, a view of one face:

An isometric view:

A cross-section view of the mechanism (no shenanigans here!):

A close-up look at some of the parts:

I ran into several problems when designing this, such as how to fit the mechanism inside of the puzzle. But they have all been resolved!
Now, the real reason i wanted to start this thread is to hear your thoughts:
1. Would you be interested in seeing a physical version?
2. If so, would you buy it?
3. Do you think the mechanism is sound? (The corner stalks are quite thin, and I can't find a way to make them bigger)
4. Is this too ridiculous to be attempted? (I can only barely imagine the cost of producing this)
Anyway, thanks guys!

I think this is grand!

However, I think the market for this puzzle would be extremely low. Maybe 1-3 copies. So I would suggest getting an investor who wants to purchase one before actually printing. Maybe Claus or someone?

And the view is obscured, but the corner stalks don't seem too thin at all.

What about hand making one?

After SuperAntoniovivaldi's video, which coincided with my solving Traiphum's Hexaminx, I expressed a wish to get a copy of your Gigahexaminx!

I was soooo disappointed to see that it is not available to buy!
So to answer your question - I would love to buy a terahexaminx but ONLY after I had bought and solved the smaller brother.

How about making and selling some more of the "Giga-" ones too?

Sorry for the gripe but I really wanted one just after I solved the "basic" Hexaminx!

Ben wasn't the designer of the Gigahexaminx, that was Ryan Binter.

Nice idea, althoug personally I think your time and money can be invested in more interesting puzzles. How thick are the shells? If they're the standard 2mm then the thickness of your corner stalks are too thin.

Oops! I apologise!
Maybe if Ryan reads this he might think about making the Gigahexaminx for sale!

Actually I talked to Ryan about this and he said that he may be able to make it available in his Shapeways Shop soon if enough people show interest, but it will take him a while to organize the pieces to print and it will be very expensive.

The hexaminx (and therefore the tera-hexaminx) requires both cuts and extensions, but I bet there are a few semi-experienced modders who would be interested in the extension bit and maybe some caps for the cut bits. So that would mean that the entire exterior would look 3D printed but the interior would be mass-produced plastic stuff. That way they would only have to do the cutting accurately with some finishing work rather than having to do all of the cutting and extending stuff...

You definitely do have a point there, and this is why I prefer hand-making puzzles with plastic sheeting rather than milliput (if I went that route with this puzzle, I would be depleting the world's supply) But i doubt anyone would ever attempt to hand make this puzzle since there is such little demand for it.
However, I've already decided to finish up this design and hopefully have it printed by the end of this month. We'll see how it goes...

I agree that there is little demand for it, and I can't wait to see it!

My reasoning was that I am not very good at modding, so maybe (off-topic) 3D-printed caps would make mods look better...

Nice idea, this has many other applications too. Curved plastic sheet anyone?