I'm pleased to present the DoDep Kit. This is a kit which allows for the construction of 680 different 5x5x5 puzzles. There are 5 different face types possible:

● Just your normal 5x5x5 face where both the face layer and the slice layer turn freely and independent of each other.

● 1 = Just the outer face layer turns. The slice layer is locked to the core.

● 2 = Both the face layer and the slice layer turn but they are locked relative to each other.

● S = Just the slice layer turns. The face layer is locked to the core.

● X = Both the face and slice layer are locked to the core. Nothing turns.

With the full set of pieces there are 680 different puzzles which can be made. That doesn't count puzzles which are mirror images of each other (as I would consider those the same solving experience). This also doesn't count different stickerings of the same puzzle.

If you limit yourself to just type "1" and type "2" faces you can make all 8 planetary versions of the DoDep 3x3x3's. These are supersets of the Planetary Crazy Plus 3x3x3's. Links:
This thread discusses individual DoDep 3x3x3's.
This thread discusses the design of the DoDep Kit.
Link will be added soon (likely after IPP) where you will be able to buy this on Shapeways.
Watch an assembly video I made for this puzzles.
Watch the YouTube Video of the finished stickered puzzle.

Solved Solved (back) A Type 1 face A Type 2 face A free or normal 5x5x5 face A Type S face Enjoy,
Carl

Aren't there 5^6 different combinations (15625 possible 5x5's) ?

RubixFreakGreg wrote:Aren't there 5^6 different combinations (15625 possible 5x5's) ?

You are over counting by alot. Many of those are the same puzzle.

Here is my math. There are 15 different types of axes possible.

(1) Free-Free
(2) Free-1
(3) Free-2
(4) Free-S
(5) Free-X
(6) 1-1
(7) 1-2
(8) 1-S
(9) 1-X
(10) 2-2
(11) 2-S
(12) 2-X
(13) S-S
(14) S-X
(15) X-X

The 5x5x5 has 3 axes. For each axes you can pick any one of these 15. However just because you pick one of these for a given axis doesn't mean you can't pick that same option for another. So the math comes down to (15+2) choose 3 or 680 different puzzles. Mirror copies are also ruled out as I don't include A-B and B-A in this list of options for the axes.

Carl

P.S. If you wanted to count the mirrored puzzles as separate puzzles the math gets tricky. One might think the list of options for the axes jumps from 15 to 25 (each of the 5 faces can be paired with all 5 face types). And (25+2) choose 3 is 2925. But this math isn't correct. If any of the axes is self symmetric, i.e. of the form A-A, you aren't creating a mirror copy but just a rotation of another puzzle. Even if all of the original 680 puzzles had mirror copies the answer would only be 1360. But that number is also too high. To get the correct number you must look at only the puzzles that have mirror copies possible. They must be formed from only these possible axes:

(1) Free-1
(2) Free-2
(3) Free-S
(4) Free-X
(5) 1-2
(6) 1-S
(7) 1-X
(8) 2-S
(9) 2-X
(10) S-X

So of the 680 puzzles only (10+2) choose 3 or 220 have mirror images possible. So if you want to count mirrors as separate puzzles then there are 680+220 or 900 total puzzles possible. At least I think I've done that counting correctly.

But mirrored copies don't always give the same puzzle (eg, top face 1, left 1 right 2; if you switch and flip the cube it's top 1 left 2 right 1, not the same puzzle). So it should be 680*2 (since flipping two axes is like flipping the third), no ?

Just out of curiosity, why not 3 for S and 0 for X?

Jared wrote:Just out of curiosity, why not 3 for S and 0 for X?

I assume that S means slice and X is used as a letter for no. If S were renamed to a number, -1 would be better IMO because 1 is the outer layer and 2 is both layers, and the second layer is also 1, hence the negative for clarification. 0 makes more sense as no layers turn. However, Carl can do what he wants with the nomenclature because the puzzles are his.

Just got back from IPP.

Yes...

1 means just the outermost layer turns on that face.
2 means just the two outermost layers turn and they are locked together.

S means just the slice layer turns. I'm talking about the layer just below the face layer, not the central slice layer.
X means nothing turns on that face.

Blank means everything is free to turn as it would on a normal 3x3x3.

This seemed like the simplest naming scheme for me. There are situations where I could see different numbering being used. If one wants to limit themselves to just 3 turning layers per axis (one dependent and two indepenadant) like a 3x3x3 I could see one putting a free (or blank) face across from an blocked (or X) face. In that case you might want to call the free face a "1" face and the blocked face could be called a "3" face. But this get's tricky and one must consider the entire axis and I'm happy with the face approach I've chosen. If someone wanted different naming I'd be happy to work with Oliver to get a custom sticker template for you.

Carl

The Slice-Only 5x5x5 is a simple fun puzzle. It corresponds to the edges, centers, and core of a 3x3x3. The orientation of the centers is visible and the edges have indistinguishable duplicates which create an ambiguity between orientation and permutation.

All the DoDep Kit is finally available in my shop.
http://shpws.me/wcmx

This kit allows for the construction of 680 different puzzles, not just the 8 Planetary DoDeps. Here is what you get in the kit.

These 10 cores: These 5 types of face centers: (The large ones are included primarily for the Mercury and Venus DoDep versions but they can be used in many other cases as well.) And these are the rest of the parts: The large faces can be thought of as face centers which are glue bandaged to its neighboring X-Centers and T-Centers. There are MANY other types of glue bandaging possible with this set of pieces. I have NOT made special pieces for ALL cases or there would literally be hundreds of other pieces. You can still make ALL these puzzles with the existing pieces but there will be some cases where you'll never be able to separate two neighboring pieces. For example you could still make the Mercury and Venus DoDeps without the included large face centers but you'd just have 9 cubies in the center of those faces (made from the regular pieces in this kit) which wouldn't be able to be scrambled.

I know there was interest in this puzzle so I've worked on this ALL day to get my last set of tweaks in and allow it to be available before October 7th.

Thanks,
Carl

Awsome Carl! I wish I had the money for this before the price hike

Well Shapeways' priceapocalypse pretty well killed this. But this post over in the Puzzle Photography group promoted me to re-package this for i.Materialise.

https://www.facebook.com/groups/1057643 ... 2491956880

It now looks like this: The current price on Shapeways is $958.78.

On i.Materialise with sinterbox it comes in at $518.56 today. I'll have to jump through a few hoops to get this into my shop and keep in mind i.Materialise deals in euros so this price will vary a bit unlike Shapeways. But its basically 46% off the Shapeways price so its certainly worth the effort getting it ported over.

For reference the pre-priceapocalypse price was $352.96.

Carl

You should just use tiny pins to connect the pieces together, so Shapeways can only charge you for one piece

E-Cubes Designer X wrote:You should just use tiny pins to connect the pieces together, so Shapeways can only charge you for one piece

I don't have an easy way to do that. And even if I did it would change the way Shapeways calculated the volume and it would still be more expensive then i.Materialise. That plus the thought of cleaning off a couple tabs on each of the 166 parts doesn't sound very fun.

By the way, this exact model has also been uploaded to Sculpteo and there it is over $1,100. That makes them even more expensive then Shapeways on this particular model.

Carl

Carl, have you tried looking into pinshape.com? They seem to even be slightly cheaper than i.materialise, and being located in the US, would reduce the shipping cost for you.

benpuzzles wrote:Carl, have you tried looking into pinshape.com? They seem to even be slightly cheaper than i.materialise, and being located in the US, would reduce the shipping cost for you.

I just upload this model to Pinshape to compare prices and it tells me:The only requirements I see are here and this model should pass all the stated requirements.
https://pinshape.com/materials-guide
and Shapeways, iMaterialise, and Sculpteo all seem happy to tell me the model is printable. As for shipping costs, everything I've ordered from i.Materialise has come with free shipping. Shipping is free on all orders above $129 or 99€.

So at least at the moment I can't tell what this would cost on Pinshape. They don't give me enough information to tell me what the issue is that they are having with my model. Has anyone here used Pinshape before? Will they email me more information then this with some images of what they think the problem areas are?

Carl

All,

The DoDep Kit is now on i.Materialise. At the moment the price is: $490.20 but this changes with the euro to dollar conversion factor.

http://i.materialise.com/shop/item/dodep-kit

This is almost half the price of the same model on Shapeways.

http://shpws.me/CFo4

And for what its worth you'll get free shipping from i.Materialise.

Just wanted to get the word out.

Thanks,
Carl

I'll have to check this out, given the lower price. Also, how well does it work when assembled as a 5x5x5?

Carl, your puzzle is fascinating but I can’t understand your counting very well. Here is mine.

I’m going to count by the number of kinds of faces used in a puzzle.
1. 1 kind of face.
5 kinds of faces, so 5 in all, nothing special.
2. 2 kinds of faces.
It is just similar to the Crazy 3*3 series which should be 8 for each case and totally 5C2 = 10(which stands for 5 choose 2) cases, so 8*10 = 80 in all.
3. 3 kinds of faces.
3.1 6 = 4 + 1 + 1
Which means that four faces are of the same type and different types for the rest two.
In this case, there are 2 possibilities for the arrangement of the four same faces. In each one, no mirrored puzzles will occur. So for 3 arbitrarily chosen types, there will be 3C1*2 =6 possibilities and the total number for this case is 5C3*6=60.
3.2 6 = 3 + 2 + 1
Here the numbers 1, 2, 3 are different so 6 cases for 3 arbitrarily chosen types. In each case, there are 3 possibilities. So it’s 6*3 = 18. The total number is 5C3*18=180.
3.3 6 = 2 + 2 + 2
As there are 2 faces for each type, we ignore the permutation of the three ”2”s. For 3 arbitrarily chosen types, there are 1+3+2 = 6 types. So totally 5C3*6 = 60.
4. 4 kinds of faces
4.1 6 = 3 + 1 + 1 + 1
(2+3)*4*5C4 = 100 cases(I’m too lazy to write down my thinking process…)
4.2 6 = 2 + 2 + 1 + 1
(4C1*3C1/2 + 4C1*3C1 + 4C2 + 4C1*3C1*2*2/2)*4C5 = (6+12+6+24)*5 = 240 cases. (well this might be wrong)
5. 5 kinds of faces
Here 6 = 2 + 1 + 1 + 1 +1
5*3 + 4C2*2*5 = 15 + 60 = 75 cases.

In all that’s 5+80+60+180+60+100+240+75=800 cases.

Sorry for my poor English and I am not sure if the whole thing is correct or not. Mirror cubes are counted two in this calculation. Maybe it’s far easier to check similar calculation of isomers of Coordination complex, but I cannot find useful info at the moment.

Linxiao

Linxiao_Xu wrote:Carl, your puzzle is fascinating but I can’t understand your counting very well. Here is mine.

<SNIP>

In all that’s 5+80+60+180+60+100+240+75=800 cases.

My math is detailed in this post.

I wasn't counting mirrored puzzles and I got 680. Counting mirrors I was getting 900. I feel confident in my 680 figure. It is possible there is a flaw in my logic where I counted 900 but I'm not seeing it. I'll have to take a closer look your logic. I think the method you choose is harder then mine but if one is careful I think it is a valid way to count them as well. So there is a mistake somewhere as 800 <> 900.

Carl

wwwmwww wrote:I feel confident in my 680 figure. It is possible there is a flaw in my logic where I counted 900 but I'm not seeing it. I'll have to take a closer look your logic. I think the method you choose is harder then mine but if one is careful I think it is a valid way to count them as well. So there is a mistake somewhere as 800 <> 900.

When you consider the ten possible axes for mirror images, I think that if any two axes are the same, you again aren't creating a mirror copy but a rotation of a puzzle you already counted in the 680.

If you count the mirror image puzzles as 10 choose 3 rather than (10+2) choose 3, you get 120 of them instead of 220, and a total of 800 instead of 900, which matches Linxiao Xu's total.

wwwmwww wrote:
I wasn't counting mirrored puzzles and I got 680. Counting mirrors I was getting 900. I feel confident in my 680 figure. It is possible there is a flaw in my logic where I counted 900 but I'm not seeing it. I'll have to take a closer look your logic. I think the method you choose is harder then mine but if one is careful I think it is a valid way to count them as well. So there is a mistake somewhere as 800 <> 900.

Carl

Carl,
I read your math again and now I could understand how you got the number 680. I was just confused by why to choose 3 out of 17. Although it's still better for me to count the three cases(3 pairs all the same; 2 pairs are the same; all three pairs are different) and you get 15C1+2*15C2+15C3 which could be simplified to 17C3 by some math.

Linxiao

Julian wrote:When you consider the ten possible axes for mirror images, I think that if any two axes are the same, you again aren't creating a mirror copy but a rotation of a puzzle you already counted in the 680.

If you count the mirror image puzzles as 10 choose 3 rather than (10+2) choose 3, you get 120 of them instead of 220, and a total of 800 instead of 900, which matches Linxiao Xu's total.

Yes... I believe you are correct. If any of the two axes are the same, the puzzle is its own mirror copy.

So it is:
680 not counting mirrors
800 counting mirrors

Thanks,
Carl

wwwmwww wrote:So at least at the moment I can't tell what this would cost on Pinshape. They don't give me enough information to tell me what the issue is that they are having with my model. Has anyone here used Pinshape before? Will they email me more information then this with some images of what they think the problem areas are?

I started a conversation with Pinshape to see why they couldn't print the DoDep Kit. Here is the latest reply...

PinShape wrote:Hi Carl,

Sorry for the delayed response! Attached is an image of the trouble regions - they seem to be within the design.

PinShape.png (199.98 KiB) Viewed 775 times

Our White Plastic is similar to the Strong White and Flexible material from Shapeways, but the rest of the plastics are not the same consistency. The print option won't work with multiple parts in a file, so you'll need to upload separate files in order to make the item printable via the professional print service.

I'd also like to let you know that, as of February 15, 2015, we will no longer be offering the professional print service. We would still love to have your design on the site as a streamed or downloaded file for our users to print at home, but I wanted to let you know in case you were only interested in the option to order printed items.

Let me know if you need any more information!

Thanks so much,

Nothing in my model is as thin as that image suggests so I believe they have an issue with their checker. But it seems to be a mute point. They don't allow multiple part models and the DoDep kit has 166 parts. I don't see anyone ordering all 166 parts one at a time. And as of today they don't offer a printing service anyways.

Oh well...
Carl

Having no idea what DoDep means I looked it up and got-
"DODEP stands for Department Of Defense Emergency Plans"

Tony Fisher wrote:Having no idea what DoDep means I looked it up and got-
"DODEP stands for Department Of Defense Emergency Plans"

Gus game me that name. Its first use in these forums is here:

viewtopic.php?p=311027#p311027

It is short for Double Depth.

Carl

E-Cubes Designer X wrote:I'll have to check this out, given the lower price. Also, how well does it work when assembled as a 5x5x5?

I've not assembled one as a normal 5x5x5 yet but it should work just fine. I have tested each face type. Before the price change at Shapeways I purchased a kit for myself that I still need to dye. I'll try to remember to text it as a normal 5x5x5 when I get dyed and stickered.

Carl