Today I have a very rare and special situation: no open orders (besides waiting for my Jades puzzles and the reserved Holey Skewb) all my puzzles have been scrambled and solved!!!!
Yesterday I solved the last outstanding, TomZ’s fully functional 3x4x5.

I have got it as a birthday gift from my wife more than a month ago.
(Nice company, right?) Because I had solved far too many new puzzles recently, I have not scrambled it until a few days back. When I got my 4x4x5 from Garrett last week and I could solve that one, I started the 3x4x5.
Some remarks about the physical puzzle:
I have bought it fully assembled and stickered with Cubesmith (smooth) tiles from TomZ. (Tiles are necessary due to little holes in the cubies, but I prefer tiles anyway, especially on WSF).It is his V3 prototype and he has improved somehow the corners in the final version. It turns very smoothly, you have to be a bit more careful when it has shape shifted, though. I cannot see much issues with the corners, but I’m sure that the final version is even a bit better.
I all fairness I have to admit that Garrett’s 4x4x5 turns a bit better, but certainly the more regular 4x4x5 allows for a more robust and smoothly turning mechanism. Both puzzles are Shapeways WSF, dyed black. I could not make a direct comparison of the complexity of the two mechanism, because I cannot disassemble the 4x4x5. This is more praising Garrett’s puzzle and no complaint about Tom’s at all.

I’m sure that not many persons on this planet are in the nice position to make this direct comparison of two very advanced cuboids.

Both are pretty demanding challenges, but the 3x4x5 is quite a bit harder. This has to do with the shapeshifting when you make 90 degree turns of the 3x5 faces. My strategy would be even very hard to describe and it is much harder to do it in practice, because the shape shifting is sooo confusing.
I mean, I have many shape shifting twisty puzzles, but this one has been the hardest to solve.
Probably, a computer program simulating this cuboid would be very hard due to the shape shifting? At least, I have not found the slightest hint in the Internet helping to get to a solution. When I had asked TomZ, if he could give me some hints, in case I would be completely lost, he answered:
For me there was a similarity to solving my first 4x4x4: I had solved the 3x3x3 a few years earlier and had assumed that it would be not so much different. Boy, was i wrong
Now, I had been warned by Tom's remark. Let me say it this way: If you have solved the 4x4x4, all other cubes are straight forward. If you have solved all mass-produced cuboids before, you have to start pretty much from scratch with this one. The 4x4x5 was a good training, though.

I have seen a post a few days back, regarding the top 5 puzzles somebody owns. One person had a 3x4x5 (fully functional?) as number three in his list. Today, I would include my 3x4x5 as well!

Who wants to share his /her opinion / experience here?

I just wanna say that this one is ON TOP of my cuboid-WANT list! And I will get it soon! maybe in September?

Then I will gladly exchange algs etc.

Although I don't own one, I'd imagine the solve would be fairly straight forward.

I don't know if you tried this method, but just solve the inner 3x3x4(which makes the shape-shifting very trivial) and then solve the outer 180 degree only 2x3x4. In fact, the start of this puzzle would be solving the innermost domino of the cuboid.

If any parity occurs on the outer 2x3x4 just swap two similar corners on the inner 3x3x4.


I've tried the 4x4x5 before and found it very difficult due to the inability to reduce it to an easier puzzle.

I can follow you for the most part, but have problems to understand: "If any parity occurs on the outer 2x3x4 just swap two similar corners on the inner 3x3x4."
Imagine this parity where you have to swap the two cubies dLF and uFR

The inner 3x3x4 is solved and the outer 2x3x4 too, less those two cubies.
There are no interchangeable "corners" on the inner 3x3x4 (I would call "corners" on the inner 3x3x4: UlF, UlB, UrB, UrF, DlF, DlB, DrB, DRF)
I can solve this situation, but it is not easy.

In that diagram, looking at the white face F, the 6 innermost cubies(or the center cubies, in this case) function as four corners and two edges of a domino. The other four corners and two edges are the blue centers, and the remaining four edges(although extended by one cubie) are the red and orange centers. Do you see the domino?

Considering the domino can have a parity of two corners being swapped, you simply swap the innermost domino corner that has the incorrectly placed orange/white piece extending from it, with the domino corner that has the incorrectly placed red/white piece extending from it.

Fixing that situation would be a rather drawn out experience, but I wouldn't call it hard by any means.

I had assumed, that you had this in mind, but you wrote

Actually, I have done exactly this, just would describe it as swapping of two edges. (One edge being two cubies: the outer edge and the centre next to it. This centre is just the corner of your inner Domino.)
My strategy had been: Bring it back to the cuboid shape. Solve as much as I can using 180° turns. Solve the rest using 90° turns, where appropriate. This has to do with the fact, that the physical puzzle turns buch better in its cuboid shape and I got often confused in the middle of an algorithm due to locking and strange shape shifting.
I find it quite an achievement that you have solved this puzzle in theory without having it as a physical object or a computer program! Congratulations
Now, that I'm a bit more fluent with solving this puzzle, I would admit that the 3x4x5 is rather more confusing than harder compared with the 4x4x5. Still, it is true that the 3x4x5 caused me more headache solving it the first time than the 4x4x5.

You have already once written that you will join me in the club of owners of specific puzzles :
The two had been a Dino Skewb and a Master Skewb. You have posted that you have got the Dino Skewb, what about the Master?

(Click the attachment to to see the full sized easy to view picture)



Jealous?

Of course it is fully functional, just like all the other cubiods in my collection! I have built FIVE 4x4x5's, all phenomenal, and THREE 5x5x4's. As for my top five hardest cubiods to solve, I place them in this order:

1. 5x5x4
2. 3x4x5
3. 4x4x5
4. 3x4x4
5. 3x3x5

I know this will change as soon as I complete some of my cubiods I am working on right now (like the 2x3x5 in the picture). That reminds me...

Can you guess my current project?





Tanner Frisby

Edit: I have finshed the project. The project was to: Clean my work space.

While we are on the topic of random cuboid projects...

Shown at an deliberately confusing angle...

After having done many solves of my 3x4x5, I have revisited the 4x4x5, to make the comparison again, how hard they are both to solve.
My verdict remains the same: The 3x4x5 is harder for me.
With the hints of Emarx it looks straight forward, but one should not underestimate the shape shifting aspects in the real world.
On the other hand, I have not needed many new algorithms solving the 4x4x5. I had to find a clean 3-cycle of the edges, though. Maybe, I was lucky finding this very quickly. The rest of the necessary algorithms, I had memorized already from other cubes or cuboids.

How to solve a fully functional 3x4x5.



Step 1. x y l2;
Step 2. (l' U2)*2 F2 l' F2 r U2 r' U2 l2 (known algorithm);
Step 3. F2;
Step 4. l2 U2 r U2 r' F2 l F2 (U2 l)*2 (this algorithm is opposite to algorithm in item "Step 2.");
Step 5. F2 l2

How I have solved this a fully functional cuboid 3х4х5.

This proposal confuses me still, but I find the discussion very interesting.

Somehow I cannot understand this solution. What do I interpret wrongly?
Following WCA notation, I get after x y a cuboid with U (white) 4x5 face, R (green) 3x5 face, F (orange) 3x4 face.
Right? Like in the left most picture of this sequence.
I'll show the result of the first few moves (as I have interpreted them) of your sequence.

The three pictures to the right show the result after a move
1. l2 l'
2. U2 (I prefer in my notes to write (Uu)2 to make clear that the topmost two visible layers are turned)
3. l'
If I continue with the sequence above, I'll end up with this (starting with a solved cube):
(F2 in the sequence above becomes (Ff)2 in my interpretation, because I can turn them together only, when the cuboid has shapeshifted!)

This is a 3-cycle of edges as I had expected looking at my 5x5x5 simulation in the other thread
I have made another 5x5x5 simulation with (Uu)2 and (Ff)2 turns.
This is the result:

The Gelatinbrain sequence is:
L&2,U'2,U'2&2,L'&2,U'2,U'2&2,F'2,F'2&2,L'&2,F'2,F'2&2,R&2,U'2,U'2&2,R'&2,U'2,U'2&2,L'2&2,
F'2,F'2&2,
L'2&2,U'2,U'2&2,R&2,U'2,U'2&2,R'&2,F'2,F'2&2,L&2,F'2,F'2&2,U'2,U'2&2,L&2,U'2,U'2&2,L&2,F'2,F'2&2,L'2&2,

This corresponds exactly to my findings on the physical 3x4x5.

Where does the difference come from?
It cannot be that we have differently behaving physical puzzles?
(Mine is a great puzzle from TomZ.)

1) For a cube 5х5х5 and for a cuboid 3х4х5:

F2 ≠ (F f)2, F2 = F2 only!!!!!

2) For a cube 5х5х5 layers U and D is not considered, as they imaginary, virtual.

Really so it is difficult to understand it? See once again attentively my algorithm on a paper.

Please, have a look at my pictures above.
F2 is NOT possible on a 3x4x5 when it is shapeshifted.
It is impossible at least on my physical puzzle.
After l2 l' (Uu)2 l' (Uu)2 my puzzle looks like this:

The next move would be F2, which is IMPOSSIBLE on my physical puzzle.
I can do (Ff)2, only
Does this really mean that we have two different 3x4x5????

Please, help from other experts!

Theoretically it is a possible situation.
But if physically it is not possible, it not a fully functional cuboid...
Means it is necessary to search for other decision on the basis of my decision. The decision somewhere beside.

Where have you got your fully functional 3x4x5? Is the move F2 in my last picture possible on your physical puzzle?

EDIT: A google search for "fully functional 3x4x5" has provided links to TomZ's puzzle (the one I have), only.
TomZ wrote in August 2009 that he has made the first fully functional 3x4x5.
Who else has made one?
Or are we talking about theoretically possible moves - like the discussed F2 - without physical representation?

We speak about the theoretically possible decision.
Such rule of elements is necessary to find when it is possible to change by places necessary (or next) elements by intermediate turn. Then to make all turns in the return order.

A theoretically possible solution does not help so much solving a physical puzzle. Right?
BTW, do you mean by the word "decision" a "solution", the way how to solve a certain problem?
(No offense meant, English isn't my mother tongue as well )

EDIT: I have asked Steryne about his version of a fully functional 3x4x5, if his can make the turn F2 on its own (without the adjacent inner slice f). This is his reply (Thanks Steryne for your agreement)Here is the picture again:

F is the orange front face looking to you. U=white.
No F2 possible, only (Ff)2 (The adjacent inner slice together with orange F with that hole.
At least TomZ's and Steryne's behave identically

I agree with this case, cuboid specially not need/possible turn any face across the sticker/tile that is under level, after shape shift.

I am one that have 3x4x5 cuboid made by self, and can't imagine how can it turn F2 if it possible
Yes! my one is impossible to turn F2 it can move only (Ff)2

The picture is my one.

Hmm if you can't solve the case on the 4x5 side, it must happened on the 3x4 side. Try to solve it there.

Don't worry, I can solve this This thread has got reanimated, because in this thread 77mouser had assumed that on the 2x3x4 a similar problem can occurr as on the 3x4x5 (I'm convinced it is different, though).
pytlivyj_1 has seen this new thread and has proposed an elegant solution for this older 3x4x5 problem. He has developed his sequence on a piece of paper and that is a big achievement, I think.
The only drawback is, that the solution cannot be done on ANY existent, physical 3x4x5

No there is no way to do a F2 in this situation. I only can turn f2. But its normal because we dont have a "super"-3x4x5 here.
Extended pieces can only move, if their extended layer is complete.

I'm not sure if this helps, but: http://www.youtube.com/watch?v=6Yjjya1BhFQ