I present to you: the worlds first fully functional 3x4x5 cuboid:



All 65 parts were printed sparse, making the puzzle extremely light. It it only 16mm on an edge, making it pretty tiny as well.

The movement is quite good and most of the puzzle is very stable, but some pieces can fall out during certain moves because of a flaw. It's still very fun to play with, and difficult to solve.




VIDEO

WOW! Verrrrrrry nice!!

Can it shape shift?

It's fully functional, so it does shift shapes by doing 90 degree turns on the 3x5 faces. My camera died before I got to take a picture of it in a weird state. I forgot to mention it in the post, but I show it changing shapes in the youtube video, and it's also in the description.

EXCELLENT, even better!

PS - access to YouTube is barred at work, so I'll take a look when I get back home.

I think that cuboids are really scary when they shapeshift ! I can't even solve a cuboid that doesn't shapeshift! I might have to get a 3x3x4 and have a go at it!

Alex

Alex, a 3x3x4 would not shapeshift. This can only happen when you have two different odd numbers, or two different even numbers of rows (assuming the axis is in the centre). For example, 2x4xn, or 3x5xn. Otherwise the blocks will not line up properly after the 90 degree turn.

Looks great! Do you always use the Japanese color scheme?

I know. I want to start with a non-shapeshifting puzzle before I make or attempt to solve a shape shifting cuboid. Unfortunately, I haven't got enough money at the moment but when I get the funds I'll try and figure out a 3x3x4.

Also, there are some exceptions. You cannot have two 'ones' even if the other number is odd and different e.g. 1x1x3 and have it shapeshift..................... unless you're Chuck Norris !

Alex

It looks wooden! I'm not that good with sizes, so can you please post a pic with a 3x3x3 for comparison? Also, am I right to say that this can be hand-made from 2 C4Y 3x3x4's in a similar manner to how the 3x3x5 is made from 2 3x3x3's? Also, I love randomly shaped cuboids. I have to say that this, along with the 3x3x4, is my favorite mod!

Wrong, this is Fully Functional.

I'm sorry I wasn't clear enough. No, I meant extended in the same fashion as a FF 3x3x5, with 'feet' at the bases of all the pieces and grooves cut in the original cube.

It could be done but it seems like a tough challenge to me, considering that you not only have to attach the outer pieces, but also the two inner 'centers'.

Hooray! Glad to see this stickered Tom! It looks great! I'll get a chance to watch the video when I get home. I've sent you an email too btw

I believe this is the rule that covers all possibilities-

A cuboid is capable of shape shifting when (two or more edge unit lengths are different and odd) or (two or more edge unit lengths are different and even) excluding cuboids with one or more edge unit length of one.

I am always curious when people ask about shape shifting. I have personally never seen a cuboid which moves on all rows and columns but doesn't shape shift when it should. You don't have to 'add' anything to make one shape shift, it simply does if it obeys the rule above.

OK, interesting, thanks. I had assumed it would depend on whether the internal cuts along one axis are compatible with the internal cuts along another axis, but if this is always the case then I see why your rule would always apply.

Is the flaw fixable? And any chance you'll be making more of these? Looks like a great puzzle.

Carl

Outstanding!

Shouldn't that exclude just cuboids with more then one edge length of one, not one or more?

And speaking of cuboids which don't shape shift when they should... what about the normal floppy cube? You need a super floppy cube to get the shape shifting property. And its the super floppy cube that makes me think the only exception should be when you have MORE then one edge with a unit length of one which I mention above.

Carl

P.S. Just realized I hadn't thought about the 1x2x3. Those typically don't shape shift either but I do think you could make a super 1x2x3 that did, not sure if anyone has.

I think it should be more than one edge length. The 1x3x3 and 1x2x3 don't shapeshift although they obey the rules, which is weird . It is obviously the mechanism though. I don't understand the floppy cube mechanism but the feet on the 1x2x3 hold the top and bottom layers on and so shapeshifting would mean that the puzzle would fall apart. They could shapeshift theoretically right?

Also, is this the cuboid with the highest number of theoretical cubies (by that I mean ignoring the mechanism i.e. 3x4x5 = 60). If not, is it the shapeshifting cuboid with the highest number?

Alex

No. A 3x5x5 has been made, and olz has made designs for much higher cuboids, such as a 9x9x7.

i see the puzzle was fully printed
how much did that cost? (if you dont mind sharing)

-Clay

Not just theoretically... I think it would be easy to build a shapeshifting 1x2x3 that functioned without falling apart. On a normal 1x2x3, the center two cubies have cutouts on two sides that accept the feet of the top and bottom layers. Couldn't you just put these cutouts on four sides of the center two cubies (instead of two) and have a super 1x2x3?

Carl

That should work. I want to make (cast) a 1x2x3 and might make a super version. Well done! You win 1 MILLION internet points!

Alex

Shapeshifting is NOT inherently inherent (it is inherent for Fisher-style mechanisms but not for the way I approach this). My first sketches (which I posted) did not allow shapeshifting by mechanism.

For example, if I had used a different profile for the 3x5 faces than for the 3x3 faces on my 3x3x5 it wouldn't have been able to shift shapes despite being fully functional. I can't recall (or look it up now) but certain faces had to have the same cutting pattern on my 3x4x5. I almost made the mistake of using different patterns.

Yes, it's fully printed but I only had to pay for the material usage (about $50) as I got it printed at a school.

well,
it looks like Tony can stay in the UK for another year

http://twistypuzzles.com/forum/viewtopic.php?p=138108#p138108

I had considered the super floppy but thought it outside the normal cuboid concept. If for example you made a 90 deg length ways turn on a 2x2x7, should we be able to turn two end cubies? Katsuhiko may say that we should but I guess there is no real answer.

well, that wouldn't work anyway, because the way the 3x3x1 is designed the corner cubies are always touching an edge since the dimensions have a difference of 2, so such a mechanism could be done to a 2x2x4 or 4x4x2 but not a 2x2x7.

Excellent puzzle Tom! It looks great and incredibly hard to solve!

great puzzle tomz!

and also
i am considering just giving you a camera!

great work!

-Clay

Excellent puzzle! It looks great and incredibly hard to solve!

Awesome! I absolutely love cuboids! Can't wait to see more!

We are talking in theory here. Otherwise the shape shifting rule would have an 'excluding over a certain size' part to it.

I really love this cuboid though and out of all the puzzles I crave at the moment, this is at the top of the craving list... I've watched the video like 3 or 4 times already

I got sidetracked by the shapeshifting discussion and almost forgot to say - an excellent first.

Why?

Such a move wouldn't add anything to the puzzle would it? I believe you would have to undo any such move before you could contine to scrable (or solve) the puzzle. On a 2x2x6 such a move might be interesting but that fits your definition of a cuboid that should be capable of shape shifting. Even there... are there any 2x2x6 puzzles that are capable of such a move? I think it would have to be a computer simulation as I see how individual cubes could end up floating in space isolated from the rest of the puzzle.

Carl

The Super Floppy cube isn't actually a cuboid... It's a cornerless 3x3 of which some edges have been removed (cut off) and two centerpieces been sunk down.

The same goes for a Super 1x2x3. It's essentially a cornerless domino:



(Top two pictures show a super 1x2x3, the bottom left picture shows the cornerless domino)

looks to me like the super floppy is the cornerless domino and super 1x2x3 is something entirely different...

Elijah, you're not quite right. I am.

Here's something for all of you to drool over... I mean... a size comparison:

TomZ, I like size comparisons with other puzzles like that. Which one were you comparing with the things on the space............................................GIMME! GIMME! GIMME!

Alex

Oh, wait a sec, I see now... it's just the cornerless domino reminded me of a shapeshifted super floppy, but I see what your talking about.
And for the picture, way to mqake me drool more!

I did a bit more thinking and made a few short animations to help me see what was going on. I guess you could (in theory) have a 2x2x7 that could do something similiar to this. Note this example is a 2x2x6 but a 2x2x7 could do the same thing.



But that is the only move that could be made after the first twist aside from undoing the first twist. In general I think all the cubies should at least maintain some contact with a face of a neighboring cubie. If the puzzle in question was a 2x2x6 such a move could be allowed and allow the puzzle to scrable in a connected fashion.



Carl

Interesting animations. I think in the first one you might be able to do that but it'd fall apart.

Alex

!? I don't get this line of thinking at all. Couldn't one then say a domino isn't actually a cuboid its a 3x3x3 in which the cubies of the center layer have been removed or sunk down (to the inside of the puzzle)? Is your 3x4x5 a cuboid? It looks and behaves like a 5x5x5 in which the cubies of two opposite faces have been removed and in which one of the center layers perpendicular to these two faces has had its cubies sunk down to the inside of the puzzle. This line of thinking seems to imply that the only real cuboids are of the form nxnxn. And note 5x5x5=125 so I'm counting the cubies of the hidden 3x3x3 on the inside. It is some of these cubies that are exposed on your 3x4x5.

This is NOT what I think of when I think of a cuboid. I do agree that a super floppy cube is a cornerless 3x3x3 of which some edges have been removed and two centerpieces been sunk down. Though I'd tend to think of those two centerpieces as removed... note they can no longer rotate on their own. Still that doesn't mean it isn't also a cuboid.

Even the 2x2x6 I've animated above is made of cubies that are just a subset of a 6x6x6.

So just why is it that you don't want these called cuboids?



So does this mean someone has already made or is working on a Super 1x2x3? Nice pictures...

Carl

Both examples are in fact easy to make, I (and I'm sure many others) could whip that up fairly easy, I might have a crack at designing tomorrow if I have a spare few minutes.

As for the comparison picture, that's simply awesome, not really that much higher than a standard 3x3, it looks really nice

Well the thought was that these are theoretical puzzles that you could play with using some software to simulate them. Not necessarily puzzles that could actually be made into physical puzzles you could hold in your hands.

Having said that I do know a way (in principle) that an actual 2x2x6 could be built that allowed both of the above moves and wouldn't fall apart. Look at my 3x3x3 here:

http://twistypuzzles.com/forum/viewtopic.php?f=1&t=6187

Just generalize this up such that you had a cage that contained a functional 6x6x6 inside the mechanism which was transparent. To make a 2x2x6 that could perform all the above moves just replace the cubies that aren't a part of the 2x2x6 with transparent cubies. As the inface between all the cubies would undoubtedly obstruct a clear view of the inner cubies I'd recommend the mechanism be made fluid tight and a trick like this could be used to make it much easier to see through the puzzle.

http://gr5.org/index_of_refraction/

It shouldn't fall apart... but I suspect it will be quite sometime before anyone actually makes something like this.

Carl

I think a 2x2x6 that performed all the moves in the second animation could work... I'm starting to picture something in my head but am not quite sure how it would work...

Wow, this is fantastic. I love it. Excellent rotation for such a big cuboid. Well done.

maybe a new topic should be made about a super 1x2x3, super 2x2x6 and such puzzles. I really want to discuss these but don't want to steal the topic more than it already has.