All,

I'd like to introduce the Neptune DoDep 3x3x3. It has an edge length of 60mm and weighs 128g.
YouTube Video

Here is some history I'd like to share:

January 31, 2011 - I came up with the notion of a multiple depth 3x3x3 and presented what I initially called the Uniaxial 3x3x3. Later the Deep Uniaxial 3x3x3. Which I will now rename the Venus DoDep 3x3x3.

Feb 1, 2011 - GuiltyBystander points out that the Uniaxial 3x3x3's (here after called DoDep 3x3x3's) are a superset of the Crazy Plus 3x3x3's and posts this picture showing how the pieces of the Crazy Plus 3x3x3's map to the DoDep 3x3x3's. February 12, 2011 - TomZ designs a mechanism which allows the Venus DoDep 3x3x3's to be built. (He actually showed me the finished Solid Works design on February 4th, 2011.) September 25, 2011 - TomZ presents the finished Venus DoDep 3x3x3.

March 17, 2012 - After working a deal with TomZ I'm able to offer the Venus DoDep 3x3x3 on Shapeways.

May 6, 2012 - I make a small modification to TomZ's design which allows the Mercury DoDep 3x3x3 to be made. At this point I'm stuck and don't see a way to make the other 6 DoDep 3x3x3's.

December 3, 2013 - E-Cubes Designer X shares his 5x5x5 design and its his design which allows me to see a way to make the other 6 DoDep 3x3x3's.

December 10, 2013 - I share the process of turning E-Cube's 5x5x5 into the DoDep 3x3x3's. Here is a mechanism picture from that thread to show you what the core of this puzzle looks like. Enjoy,
Carl

All,

I will be offering this and ALL the DoDep 3x3x3's in my Shapeways Shop soon. I want to make a few tweaks to the design to make it more tumbling friendly first. I plan to make a separate model for each of the versions. For the Mercury and Venus versions I'll be sticking with the current TomZ design as it will be a cheaper model with fewer parts. If anyone is interested in a kit which would allow the construction of any ONE of the 8 DoDep 3x3x3's let me know and I can offer that as well.

Here is the basic sticker template: Olivér has also made a new version of the sticker template for the Mercury and Venus puzzles which looks like this: And I've also asked Olivér to offer a set of printed stickers which look like this: With these I intend to replace one of the corner stickers on the white face to make it easier to identify each of the DeDep 3x3x3's without the need to turn faces to understand which puzzle one is holding.

Note to Andreas. I haven't cleaned up the above pictures yet. Once I get the Planetary stickers from Olivér I plan to take some better pictures of the puzzle and I'll replace the ones above with those. So if you could hold off a few weeks before you add this to the Museum, I'll have some better pictures for you.

Also if there is anyone out there interested in an entire set of all 8 versions (aside from me) let me know. I plan on putting my normal markup on each puzzle but if someone wants all 8 (or even just several) I'd like to offer them a way to complete the set without me getting a full markup on each puzzle (if they order them though Shapeways). I envision it would work something like this. Someone buys one of the puzzles off Shapeways and PM's or emails me their order# or other proof that they purchased one of the DoDep 3x3x3. And I would then provide them with a link to the remainder of the puzzles they are interested in from the set at a significantly reduced price.

Enjoy,
Carl

Since I was absent in 2011, I am really scratching my head about the mechanism here. I'll have to stare at the pictures for a while.

But this looks amazing. Nice work. What a unique idea.

Well done Carl, it has been interesting to watch the development of this series of twisties. And I got to name someone else's design for the first time Well chuffed!

Great puzzle, Carl! As a fan of circle puzzles, I love this concept. I'm guessing these are very difficult puzzles. Have you tried solving any of them yet?

I would like to issue the challenge to any programmers out there: I would love to have a simulator for this!!

Very very interest puzzle!

Fascinating. Can the puzzle be fully scrambled?

Oskar

Oskar wrote:Fascinating. Can the puzzle be fully scrambled?

Short answer... yes.

Long Answer... depends on what you mean by fully scrambled.

The Mercury and Venus versions using TomZ's design approach only have surface pieces plus a single hidden core pieces. Any two surface pieces can be seperated with his design. However you could make a Mercury and Venus version using a different core with the same pieces used in the Neptune version. If that was done you would have 9 surface cubies on two faces which couldn't be sererated. These would be the large face centers you see on the current Mercury and Venus versions. But also keep in mind there are also hidden 3x3x3 pieces inside the puzzle aside from the core. These hidden pieces could NOT be fully scrampled. The hidden 3x3x3 inside a Venus version would be reduced to a 1x1x3 which only allowed oppose faces to turn. The hidden 3x3x3 inside a Mercury version would be reduced to a 1x1x2 which only allowed a single face to turn.

Let's look at the Neptune DoDep 3x3x3 specifically. This puzzle has 5x5x5 like surface pieces. These can be fully scrambled. Pick any two surface pieces and they can be seperated with a couple of turns. But this puzzle also has hidden 3x3x3 like pieces on the inside in addition to a core. On the Neptune version this 3x3x3 is reduced to a Fuzed Cube. So there is a grouping of a 3x3x3 corner and three 3x3x3 edges which can NOT be scrambled on the inside. As you can't see these pieces during a solve you have now way to know this so that is why I'd say yes you can fully scramble this puzzle. There may be some face center parity issues that would keep a super version from having the same number of states as a Super 5x5x5, I'm not sure. But if one just looks at the normal version, I believe the Neptune DoDep 3x3x3 has the same number of states as the 5x5x5. I haven't proven that though in case anyone wants to check.

This also leads into the question... Are these DoDep puzzles the definitive Super Set of the Crazy Plus 3x3x3 puzzles? The answer is no. The inner 3x3x3 pieces can't be solved in this set. I need to finish my Real 5x5x5 first and then once I do that I can make the Neptune DoDep Real 3x3x3 or the Multi- version of this puzzle. That would allow you to solve the inner Fused Cube at the same time. Though the cost difference between a set of Crazy Plus 3x3x3's and a set of DoDep 3x3x3's is likely to me smaller then the cost difference between a set of DoDep 3x3x3's and a set of DoDep Real 3x3x3's.

Oh... and I'm still looking for a set of the original colored plastic Crazy Plus 3x3x3's myself. If anyone has a set they are willing to sell or trade PM me.

Carl

Oskar wrote:Fascinating. Can the puzzle be fully scrambled?

After a quick run of GAP I found that this puzzle has as many permutations as the 5x5x5:
2582636272886959379162819698174683585918088940054237132144778804568925405184000000000000000
This number assumes that the T-pieces and the X-pieces can be distinguished. There is no orientation of faces included.

Andreas Nortmann wrote:After a quick run of GAP I found that this puzzle has as many permutations as the 5x5x5.

Nice! And thanks! If you can do this easily (if not I can do it... just need to find the time) would you mind comparing the Super Neptune DoDep 3x3x3 to the Super 5x5x5? Here I suspect the Super 5x5x5 may have more permutations. With the Super Neptune DoDep 3x3x3 having two types of face centers I suspect it may have some parity restrictions that the Super 5x5x5 wouldn't have. But that is just a guess.

I know the Super-Multi Neptune DoDep 3x3x3 has fewer permutations then the Super-Multi 5x5x5. Inside a Super-Multi 5x5x5 you have a full 3x3x3. Inside a Super-Multi Neptune DoDep 3x3x3 you just find a Fused Cube.

Carl

wwwmwww wrote: If you can do this easily

No. I can't do this easily.
I also edited my earlier post.

Ok... I played with GAP today. Here is what I produced:



If needed here are some definitions:

Normal = All type 1 Faces
Circle = All type 0 Faces



Crazy Plus 3x3x3 = Normal Puzzles as defined above.
Super Crazy Plus 3x3x3 = A Crazy Plus 3x3x3 where each pieces has a unique position AND orientation in the solved state. Face center orientation is considered.
DoDep 3x3x3 = My DoDep series stickered with normal stickers.
Super DoDep 3x3x3 = My DoDep series stickered with super stickers.
Multi DoDep 3x3x3 = A DoDep puzzle viewed as a Multi-5x5x5 (with a 3x3x3 inside). Normal stickers applied to the 5x5x5 and the 3x3x3 inside.
A Super-Multi DoDep 3x3x3 = A DoDep puzzle viewed as a Multi-5x5x5 (with a 3x3x3 inside). Super stickers applied to the 5x5x5 and the 3x3x3 inside.

For the DoDep calculations I also included a 5x5x5 for comparison. For example the Super-Multi 5x5x5 would be my Real5x5x5 puzzle.

Some interesting observations.

(1) Except for the Venus and Mercury versions the Normal DoDep puzzles have the same number of permutations as a Normal 5x5x5.

(2) Except for the Venus and Mercury versions the Super DoDep puzzles have HALF the number of permutations of a Super 5x5x5. So there is an interesting added parity to the face centers as I suspected.

(3) Only the Jupiter Multi-DoDep puzzle has the same number of permutations as a Multi-5x5x5. This is due to it being the only version that allows you to fully scramble the inner 3x3x3.

(4) The Jupiter Super-Multi DoDep puzzle comes closest to the number of permutations of the Super-Multi 5x5x5 but it is still a factor of 4096 short.

I've attached the GAP files and a text file containing the above numbers. If anyone wants to double check the calculations please let me know if you get the same numbers.

Thanks,
Carl

It's great to see these puzzle after so long since their initial conception. Your persistence on the topic is admirable.

themathkid wrote:Have you tried solving any of them yet?

I don't watch the solving subforum too closely but I'm not sure if anyone's done any work toward solving these. I've only managed to solve the Mercury and Jupiter Crazy Plus 3x3 so I'm quite behind on even the originals. Because of the varying depth, I'm curious if you could use techniques similar to those needed to solve TomZ's Chimera Cube.

wwwmwww wrote:(2) Except for the Venus and Mercury versions the Super DoDep puzzles have HALF the number of permutations of a Super 5x5x5. So there is an interesting added parity to the face centers as I suspected.

This is by far the most interesting statistic. The other ones make sense.

Would this same mechanism work to make a TriDep?

GuiltyBystander wrote:This is by far the most interesting statistic. The other ones make sense.

I believe this means that for the puzzle to be solved (except for the face centers) then both the type 1 and type 2 face centers need to be in an even parity state. With a Super 5x5x5 there is only one type of face center so a 90 degree clockwise rotation of any face can be offset by a 90 degree counter-clockwise rotation of any other face. I don't believe this is the case for the DoDep puzzles.

GuiltyBystander wrote:Would this same mechanism work to make a TriDep?

Yes... I think so. And I'll be giving that a shot after I get my Real 5x5x5 finished.

Carl

All,

I now have the Neptune DoDep 3x3x3 on Shapeways.
http://www.shapeways.com/model/1893447/ ... 3x3x3.html

And I'm also offering a very special deal on a full set of all 8 DoDep puzzles through May 12th. See details here.
http://twistypuzzles.com/forum/viewtopi ... =4&t=27228

Thanks,
Carl