I came across this old post by Sandy- viewtopic.php?p=9537#p9537 . He talks about making a proportional high order NxNxN puzzle by embedding it inside a transparent sphere saying it would definitely work.
The world has come a long way since then and I wondered if anyone had any new opinions on this idea. I don't quite see how it could work but I am not an expert on mechanisms like many of you guys. If the theory is sound though I am sure we are now technically able to construct such a puzzle. Given the choice I think I would prefer a perfectly proportioned 9x9x9 (for example) with a clear shell to a pillowed or unproportioned "flat" version.
Like I say, I don't see how it would work but if it does then I can't help thinking a full sphere would not be required.

I guess it would be like taking the 17x17x17, and making part of the extra thick outer layers transparent so the only portion left that is not transparent is a perfectly proportionate cube. Unfortunately that would result in the inside cube being olzed, so you might just as well do without the outer transparent parts.

Yes, that's kind of what I thought. A proportioned NxNxN would have to exist somewhere within the puzzle for it to be made visible.

That is correct, of course. One simple solution is to have the visible pieces of the proportional NxNxN to be extended with transparent material into a sphere, and enclose it with a transparent sphere, Houlis style.

If you want a true TP mechanism, you could extend the concept of the Void Cube, Hollow Cube and Void 5x5x5 to NxNxN, and extend the pieces with more transparent material to the inside up till the proportional NxNxN.

Polycarbonate would be probably the material of choice, being strong and window-transparent. Because of its low scratch-resistance, a hard coating would need to be applied. That combination works for contact lenses and sport-hall windows, so it should work as well for an inverted proportional NxNxN.

Note that the inside of the proportional NxNxN can be completely hollow, you would just need to paint the faces of the cube from the inside. I tried this technique with acrylic. It looks very nice, as the visible painted surface is perfectly flat. The mechanism would then be completely out-of-the-box.

Oskar

I can see how that would make the puzzle but how would you make moves?

Aaaaand now I want to see an olzed proportional 17x17x17 cube.

Isn't that a contradiction?

Nah, proportional only means "the edge is evenly divided".

It means everything in correct proportion. All squares, cubes, equal cubie sides etc.

You take a Leprechaun, put him inside the hollow cavity constituting the proportional NxNxN, and instruct him to make (three) moves for you. Alternatively, you consider my suggestion for a true TP mechanism ...

Oskar

Yes I saw that but don't understand it.

I get Tony's point. I don't really understand this mechanism idea.
I just don't see why there actually is a proportional 7x7x7 cube inside a 7x7x7 cube that is not proportional. I am pretty sure there isn't. There's "simply" a mechanism. One that can't be proportional. Making a large clear 7x7x7 sphere and only coloring up to a point inside where the pieces form a "still proportional 7x7x7" isn't possible because at the deepest point where pieces start to exist they already aren't proportional.

Although I must say I just blindly believe Oskar to be honest. Despite not understanding his logic.

Perhaps these sketches help conveying the concept? It is a straightforward extension from the Void 5x5x5, which in turn was based on the now classic Void Cube.

Oskar

Ah so the mechanism is within the clear extensions, I see it now. So once we have clear 3d printing we can start making these I guess.
It is also the solution to a giant negative 3x3x3 idea I had where you are actually inside a cubic void with the coloured squares all around you.

The air at the gaps will still cause a lot of reflections, making the mechanism rather visible and non-transparent. C.f. how transparent are "transparent" Rubik's Cubes? We could for instance keep the cube submerged in index-matching liquid. Alternatively, we could use anti-reflection coating.

Oskar

Or make the parts out of air, like my imaginary proportioned 17x17x17.

Wow that works? So they are made proportional at the very inner wall of the void hole. Great, thanks for the pictures.

So all we need do is turn it inside out and we have unlimited proportional NxNxNs.

You might be onto something.
What if we find the radial mirror image of each point of the mechanism with respect to the points on a bigger cube surrounding the internal NxNxN, so that the outer parts would be reflected inwards to the inside of the puzzle and the inner parts would be reflected to the outer surface.
Each part would remain continuos (only mirrored), so I'm guessing the resulting mechanism would still work. (Or maybe it would lock up, I'm not sure about this)
But you would definitely get a proportional NxNxN looking puzzle!

Edit: I did not consider the points inside the proportional NxNxN!

Not sure how I missed this thread last month. But thanks to Tony's post here I've now found it.

Anyways... back in 2007 I saw this video:

https://www.youtube.com/embed/HyxLQpraM88

I can't say that I understand the language so I have no idea what the song is about but the background of this video appears the be the inside of a void 5x5x5. This may be the same idea that Tony is calling a "giant negative 3x3x3". Anyways it was the video that prompted me to come up with this design back in January 2007.

New 3x3x3 well sort of... (WARNING: Pics and animations)

And in that same thread I show how the idea can be applied to make a proportional 7x7x7. Then I stated:

But you can bandage that 9x9x9 into a 7x7x7 and you have basically the same idea Oskar presented above. I just made the shell one order higher so that the faces could appear to turn as seen from the inside (as seen in the video above).

Carl

P.S. Here is what you get if you cut Oskar's corners to get the 11x11x11 that contains a proportional 9x9x9.