I'd like to present the finished and stickered Bubbloid223 puzzle.

The puzzle weighs in at 144 grams.

The edge lengths are:

18*(0.5+3*(1+sqr(2))/2) ≈ 74.18mm
27*(1+sqr(2)) ≈ 65.18mm

So the outer most edge pieces are 9mm wide. All the pieces of the Bubbloid123 are reused here unchanged except for the core.

In this thread I presented some pictures before the puzzle was completed.
http://twistypuzzles.com/forum/viewtopi ... =9&t=26072

You Tube Video
http://youtu.be/gR3R99zSYKw

You may purchase this puzzle in my Shapeways shop here:
http://shpws.me/vZme

Solved... Mid-turn Partially scrambled Several corner in mid-turn at the same time A family picture of the Bubbloids where each corner cut is 3 edges deep Enjoy,
Carl

I love it! I can't wait to do a family photo.

Will this be your last cuboid Bubbloid?

Have you considered trying to do a "master" version where each corner has two layers to turn?

Brandon Enright wrote:I love it! I can't wait to do a family photo.

I am eager to see it. I have to say I'm very pleased with how well these have been received. I've sold 3 complete sets so far... including the one pictured above. That will get getting packed up and mailed tomorrow. I was afraid these were getting to be too expensive.

Brandon Enright wrote:Will this be your last cuboid Bubbloid?

I haven't even started designing the set with the corner cut 4 edges deep but seeing as these are selling as well as they are I suspect I'll take a shot at that set at some point. I have several other puzzles I want to finish first.

Brandon Enright wrote:Have you considered trying to do a "master" version where each corner has two layers to turn?

Yes... I've at least thought about it. There are a couple reasons why I doubt I'll do it.

(1) Adding those extra turns would actually make the puzzles easier and these are already easier then the Rubik's cube so I don't want to make them too easy.

(2) Those cuts which appear like that should allow these extra turns don't line up. The cuts closer to the corners are made from 3 separate spheres which don't share the same center and none are centered at the corner. You'd need to add a new spherical cut with a radius 9mm less that was centered on the corner to allow this. That would create several very thin slivers cut from the existing pieces. If left in I think they'd simply be too small to be stable and if they were taken out to fudge the puzzle I think the whole puzzle would be too loose. I haven't actually tried to design these pieces but that is what I think would happen.

Carl

Oskar likes to ask questions at the end of his videos. I figured this would be a good place to ask some Bubbloid trivia.

To date I have made the following:
Bubbloid112
Bubbloid122
Bubbloid123
Bubbloid223
Bubbloid233

(1) Why have I not made a Bubbloid111?
(2) Why have I not made the Bubbloid222 or the Bubbloid333?
(3) Why have I not made the Bubbloid113 or the Bubbloid133?
(4) If you take out the outer most edges of the Bubbloid233 you still have a functional puzzle, but it amounts to a shape mode of an existing puzzle. What is that puzzle?
(5) If you take out the outer most edges of the Bubbloid223, what does this puzzle reduce to?
(6) If you take out the outer most edges of the Bubbloid123, what does this puzzle reduce to? This one is a little tricky.
(7) If we step up to the puzzles where the corner cuts are now 4 edges deep, how many new/unique Bubbloids are added at this level? What are they?

I know the answers to 1-6 off the top of my head. I'd have to think a bit more before I was sure of the answer to #7 myself.

Enjoy,
Carl

wwwmwww wrote:Oskar likes to ask questions at the end of his videos. I figured this would be a good place to ask some Bubbloid trivia.

Glad to oblige.

To date I have made the following:
Bubbloid112
Bubbloid122
Bubbloid123
Bubbloid223
Bubbloid233

wwwmwww wrote:(1) Why have I not made a Bubbloid111?

That would just be a rainbow cube. Or more specifically, the curvy compino.

wwwmwww wrote:(2) Why have I not made the Bubbloid222 or the Bubbloid333?

This would also result in the curvy compino, because the smaller edge pieces would never be cut up and you would still end up with an overlap of one piece.

wwwmwww wrote:(3) Why have I not made the Bubbloid113 or the Bubbloid133?

For the previous reason, this would just be a Bubbloid 122/112.

wwwmwww wrote:(4) If you take out the outer most edges of the Bubbloid233 you still have a functional puzzle, but it amounts to a shape mode of an existing puzzle. What is that puzzle?

It must be the Bubbloid 122. (unless, of course, this is a trick question)

wwwmwww wrote:(5) If you take out the outer most edges of the Bubbloid223, what does this puzzle reduce to?

This must be the Bubbloid 112.

wwwmwww wrote:(6) If you take out the outer most edges of the Bubbloid123, what does this puzzle reduce to? This one is a little tricky.

Now you've got me thinking. I'm going to guess the Bubbloid 112. (I'm wrong )

wwwmwww wrote:(7) If we step up to the puzzles where the corner cuts are now 4 edges deep, how many new/unique Bubbloids are added at this level? What are they?

In this case we can have overlaps of 4 pieces now. Here's what I think we get:
134, 234, 334, and 344.

benpuzzles wrote:

wwwmwww wrote:(1) Why have I not made a Bubbloid111?

That would just be a rainbow cube. Or more specifically, the curvy compino.

Yes... it has already been made. Here is one. I may make one for myself someday... but I wouldn't feel right offering it for sale.

benpuzzles wrote:

wwwmwww wrote:(2) Why have I not made the Bubbloid222 or the Bubbloid333?

This would also result in the curvy compino, because the smaller edge pieces would never be cut up and you would still end up with an overlap of one piece.

Correct.

benpuzzles wrote:

wwwmwww wrote:(3) Why have I not made the Bubbloid113 or the Bubbloid133?

For the previous reason, this would just be a Bubbloid 122/112.

Yes. The Bubbloid113 would be the same puzzle as the Bubbloid112 and the Bubbloid133 would be the same puzzle as the Bubbloid122. There would be pieces you'd never be able to separate in a scramble.

benpuzzles wrote:

wwwmwww wrote:(4) If you take out the outer most edges of the Bubbloid233 you still have a functional puzzle, but it amounts to a shape mode of an existing puzzle. What is that puzzle?

It must be the Bubbloid 122. (unless, of course, this is a trick question)

Yes... solving all but the outer most edges of a Bubbloid233 is the same puzzle as solving a Bubbloid122.

benpuzzles wrote:

wwwmwww wrote:(5) If you take out the outer most edges of the Bubbloid223, what does this puzzle reduce to?

This must be the Bubbloid 112.

Again correct.

benpuzzles wrote:

wwwmwww wrote:(6) If you take out the outer most edges of the Bubbloid123, what does this puzzle reduce to? This one is a little tricky.

Now you've got me thinking. I'm going to guess the Bubbloid 112. (I'm wrong )

Yes, you are wrong. Take out the outer edges and count the next outer most edges shared between adjacent corners. Then sort from smallest to largest. You will have a BubbloidXYZ where X <= Y <= Z. Then ask yourself if I've built that Bubbloid. If not... why not?

benpuzzles wrote:

wwwmwww wrote:(7) If we step up to the puzzles where the corner cuts are now 4 edges deep, how many new/unique Bubbloids are added at this level? What are they?

In this case we can have overlaps of 4 pieces now. Here's what I think we get:
134, 234, 334, and 344.

This is the hard one. I think the Bubbloid124 may also need to be in this list. I almost need to sit down and model all of them to be sure. GuiltyBystander made some very nice images of a couple of the Bubbloids with corners cut 5 edges deep in this thread. (here and here) His Bubbloid125 looks to me like it would reduce to the Bubbloid124 but I don't think this is the same puzzle as the Bubbloid123.

GuiltyBystander, what software did you use to make those images? Would you mind making some images of the new/unique Bubbloids which have 4 as their largest overlap?

Thanks,
Carl

wwwmwww wrote:

benpuzzles wrote:

wwwmwww wrote:(6) If you take out the outer most edges of the Bubbloid123, what does this puzzle reduce to? This one is a little tricky.

Now you've got me thinking. I'm going to guess the Bubbloid 112. (I'm wrong )

Yes, you are wrong. Take out the outer edges and count the next outer most edges shared between adjacent corners. Then sort from smallest to largest. You will have a BubbloidXYZ where X <= Y <= Z. Then ask yourself if I've built that Bubbloid. If not... why not?

It would be the 012, right? This would be two separate dual-origin puzzles with 4 axes each siamesed together. It hasn't been built because it's kind of redundant.

rayray_2561 wrote:It would be the 012, right? This would be two separate dual-origin puzzles with 4 axes each siamesed together. It hasn't been built because it's kind of redundant.

Correct. I had for a while considered making one half of this puzzle... with just 4 turnable corners. But technically you can play with and solve that puzzle with either the Bubbloid112 or Bubbloid122 if you pick the correct 4 corners and just never turn them during a scramble or solve. So I just didn't feel it would be interesting enough as a separate puzzle. Basically the only reason I was considering it was I thought if I made it small enough it would have few enough parts that I might be able to afford to print a bunch of them that I could use as an exchange gift at an IPP. The half puzzle, if I ever made it I'd probably call the Bubbloid12. That way the Bubbloid012 would simply be two siamesed Bubbloid12 puzzles. But I have my doubts that I could get the costs low enough that I could afford to print a 100 copies even of a small version.

There is also another very interesting thing about the Bubbloid12. It relates to the distinction between doctrinaire puzzles and non-doctrinaire. I believe this puzzle can blur that line a bit. Let me make some pictures and I may start a new thread to show you what I mean.

Carl

Why do the insides of these edges curve inward?

rubikcollector123 wrote:Why do the insides of these edges curve inward?

You asking about the red curve? If so, that is created by the filleting process. The piece before filleting comes to a very sharp point at the edge of the puzzle, which would be too thin to 3D print without filleting. Does that answer your question?

Carl

I think that is what he what he is asking about.

I wonder if it was intentional, or just due to solidworks? I was filleting puzzle pieces before and instead of doing a normal fillet, it caused a dip like this. I managed to work around it, but it was really weird and I have no idea why it happened.

wwwmwww wrote:

rubikcollector123 wrote:Why do the insides of these edges curve inward?

You asking about the red curve?

Curve.png

If so, that is created by the filleting process. The piece before filleting comes to a very sharp point at the edge of the puzzle, which would be too thin to 3D print without filleting. Does that answer your question?

Carl

Yes it does. I get it now.

I've been meaning to post on your threads for a while now, but every time I got around to it, it felt like the threads had gone cold. So for starters I'll say I'm really excited about all the puzzles you've been working on and I hope you get them mass produced because the are really interesting puzzles. I know it's been a long road from conception to realization for most of them.

wwwmwww wrote:Bubbloid125 looks to me like it would reduce to the Bubbloid124 but I don't think this is the same puzzle as the Bubbloid123.

Yes, I agree that the 125 is the same as 124 and it is definitely different from the 123.

wwwmwww wrote:GuiltyBystander, what software did you use to make those images? Would you mind making some images of the new/unique Bubbloids which have 4 as their largest overlap?

I made those kind of manually with Rhino which I don't have access to anymore.
Back in that other thread, I did write a small java program to explore what's active with various bubbloids. It only renders the section that moves on the largest overlap but that's the key part and should be enough to imagine the whole cube.
http://landonkryger.com/rubik/DinoCuboid/DinoCuboid.jar

I don't know if there's any quick easy way to calculate what the reduced version of a bubbloid is. I have a hacky/cheaty way in mind that might work, but not completely sure about it.


Your turn for some questions.
1) I know you're a big fan of super puzzles. Do you have any plans for how you could super sticker/shape mod to make every piece unique? They have a lot of pieces on them that can be swapped without noticing. The standard super stickering schemes don't look like they'll work here.

2) Have you done much solving with these? The piece orbits can get quite large and tangled on these bigger ones. I image that even simple commutators for these must be 10 or 12 moves long at least. The hardest deep puzzle I've solved so far is probably Starminx with a 10 move algorithm for the points and when you add in 2-3 setup moves, it can get really confusing. If you make the Bubbloid344, you'll have to layer several commutator on top of each other just to isolate 1 piece.

I need to go digest your other thread now. I suspect the questions there are going to be harder to answer.

GuiltyBystander wrote:So for starters I'll say I'm really excited about all the puzzles you've been working on and I hope you get them mass produced because the are really interesting puzzles.

Thank you very much.

GuiltyBystander wrote:Back in that other thread, I did write a small java program to explore what's active with various bubbloids. It only renders the section that moves on the largest overlap but that's the key part and should be enough to imagine the whole cube.
http://landonkryger.com/rubik/DinoCuboid/DinoCuboid.jar

Thanks. Yes this helps alot. I am now about 99% sure that the new Bubbloids at the next level are the Bubbloid124, 134, 234, 334, and 344. And while the Bubbloid122 and 112 used all the same parts (except for the core) just like was true for the Bubbloid123, 223, and 233, this isn't exactly true for this next level up. The Bubbloid124 only has 3 types of edges. The Bubbloid134, 234, 334, and 344 all have 4 types of edges. And the 3rd type of edge of the Bubbloid124 would bandage the others. It is basically a group of 4 edges from the other bubbloids bandaged together. I really want to make this set now... it seems things are just starting to get interesting.

GuiltyBystander wrote:Your turn for some questions.
1) I know you're a big fan of super puzzles. Do you have any plans for how you could super sticker/shape mod to make every piece unique? They have a lot of pieces on them that can be swapped without noticing. The standard super stickering schemes don't look like they'll work here.

I've done some thinking on this but not an incredible amount. I'll probably double that here. While I do like super puzzles I tend to also like difficult/tricky problems too. And there are times making a puzzle super I think makes things easier as it gets rid of some parity issues which I think are interesting in their own right. Also on these puzzles (the Bubbloid123, 223, and 233) there are 3 types of edges but not ALL the edges of a given type can be exchanged with all the others of the same type. Many of the identically stickered pieces can not be interchanged as they are in different orbits... but some can. So you are correct, these are not super versions. To make a super version with stickers you could do several things:
(1) Make it a picture puzzle and put a picture on each face. Here is a Super Bubbloid122.
(2) Print numbers on the pieces in some order that needed to be reproduced when solved.
There are also ways the shape of the puzzle could be varied.
(1) The multi-origin property that I use to make these isn't the only way to make Bubbloids. Oskar has shown that if the puzzle is a sphere you can make the same puzzle where all the axis cross at just a single point. The reason I don't do this is that to keep all similar edges the exact same shape then the final puzzle must be a sphere. But you can shape mod the sphere back into a block. You generate many different shapes this way but you may still have to bump the origin off center to assure all pieces have a unique shape. I just thought about it for a bit and there should never be issues with over hang bandaging regardless of the shape. The cuts would all be conical out from the origin. So I bet you could do this and make every piece a unique shape if you wanted to. It would be alot more CAD work to design all those pieces. It would never stand a chance of getting mass produced. And I don't think it would look as nice. But yes it could be done.
(2) You may be able to apply the bump method to the multi-origin design but there the cuts are spherical and extending or truncating the faces I think could get tricky. Plus to make the similarly stickered pieces different shapes you couldn't just keep the new faces parallel to the old ones so your nice rectangular block wouldn't be a nice rectangular block any more.

If someone really wanted a shape modified super bubbloid I think I'd personally prefer option (1). At least there I think you could still cut it into a block when you were done. Though I'm not sure the axes of rotation would come out of the point of all the corners if the origin was off center from the center of the block. I just haven't designed a Bubbloid this way before. To the main point of your question... no I didn't have any immediate plans to make a Super Bubbloid. Having typed all this up I'm convinced that is could be a fun CAD project but seeing the large number of pieces in one of these puzzles and knowing how much work it would be to make all those unique pieces I doubt I'll be doing it any time soon. But if the interest is there I can add it to the to-do list. Something tells me the powder drain holes on the parts will look like numbers. I think just assembling a puzzle like that with all unique pieces would be a nightmare unless there was a method of telling where each pieces goes.

GuiltyBystander wrote:2) Have you done much solving with these?

That is an easy one. I have ALMOST solved a Bubbloid122. And to date that is the only one of these Bubbloids I have even tried to solve. In high school (many moons ago) I could solve a 3x3x3 in under a minute. But I had just memorized the solution from a book. I've long since forgotten that solution and today I can intuitively get the top two layers with ease. The bottom layer I still usually end up having to resort to looking up moves on line. I keep telling myself someday I will develop my own solution to the 3x3x3. I know how. It is just that I enjoy designing mechanisms more and with what little free time I have I am much more likely to work on a design then I am to sit down and try to solve a puzzle. So no... I can't say too much about the solving side of things. I've had the Bubbloid122 and Bubbloid112 at the last several IPPs and I've seen them solved many times. And I've sold well over 20 or so Bubbloid122 puzzles alone (maybe even closer to 30 now) so I know there are people out there solving them. Bob Hearn is one of those I've seen solve the Bubbloid122 or 112. Unfortunately the Bubbloid123, 223, and 233 were not yet stickered when I had them with me at this last IPP.

Carl

I've updated my program with a couple new features. Same link as last time.

• Calculate the most reduced version of a dino cuboid
• Render the full cuboid form
• Find the next/previous irreducible cuboid

wwwmwww wrote:I really want to make this set now... it seems things are just starting to get interesting.

I've been doing a bit of exploring and found that 124 belongs to a series of interesting puzzles I'd like to call the Fibonacci Dino Cuboids. Take three sequential Fibonacci numbers, subtract 1 from each and use them for the overlap amounts. For example here's 12-20-33Every large piece is the size of the two pieces smaller than it. It reminds me of the tiling of Fibonacci squares used to create a spiral. I find the pattern quite pleasing.

I've done some math and if you set the overlap sizes to [1, phi, phi^2] (where phi is the golden ratio), you'll end up with a version with the same ratio of piece sizes as above but it will also jumble and have an infinite number of pieces. The topic of jumbling makes me wonder if perhaps one way to get past the limit of 5 edges per corner is to bandage some of the outer layers. Though identifying what to bandage would difficult and I'm not sure you'd end up with anything more interesting than what's possible without bandaging.

It's too bad that the larger Fibonacci dino cuboids can't be made as Bubbloids. I like that the 2-4-7 has the same number of piece types as a 2-3-4. You may have to think about shaped mods soon if you want these. Hopefully pillowing doesn't distort your distinct look too much. I keep trying to imagine what it would look like on a FTO, but all I can think about is how you've created corners and I don't know what those do.