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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Dec 04, 2010 3:46 pm 
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ortwin wrote:
Gelatinbrain my suggestion for a further puzzle is a quite obvious one- at least for me.
3.1.3 (4x4x4) combined with
3.2.1 (skewb) with
3.2.4 (dino) with
3.3.1 (helicopter) and with
3.3.7 (little chop)

Four layers in faces, edges and vertices.

You have some puzzles that are close, but not quite what I mean: 3.7.2 , 3.7.5 ...

Or did I miss something?


GB has added such a puzzle: 3.7.9. What a massive puzzle!


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Dec 04, 2010 5:08 pm 
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bmenrigh wrote:
Maybe I'm in the minority but I don't really like cuboids, bandage cubes, the crazy plus, siamese cubes, and other puzzles that have blocking/limited/non-symmetrical moves. I don't like them for the same reason they are hard to program and hard to solve, a sequence that can be applied to one part of the cube might not be able to be applied if the puzzle changes orientation.



I don't like these things either. I don't want to mess up my code by indiscriminately adding everything. It's better to fix a border. First I'd like to exhaust most basic twisty puzzles and then classify them.
I don't have yet my own clear definition of twisty puzzles, neither a good method to classify them. But most basic twisty puzzles are certainly symmetrical ones.
They are far more numerous than I first imagined.
In the Euclidean world, Platonic solids and derived Archimedean solids(shape is not essentiel) belong to this category, the tesseract and other 4D extentions of platonic solids too.
My 2D puzzles 7.1.2 & 7.1.3 should also classified into this group, but not 7.1.1(those who already solved them should know why :wink: ).
A twisty puzzle is not necessarily a geometrical puzzle.
I think abstract twisty puzzles also could exist. All depend on the definition...

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Dec 04, 2010 5:51 pm 
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gelatinbrain wrote:
They are far more numerous than I first imagined.
In the Euclidean world, Platonic solids and derived Archimedean solids(shape is not essentiel) belong to this category, the tesseract and other 4D extentions of platonic solids too.
My 2D puzzles 7.1.2 & 7.1.3 should also classified into this group, but not 7.1.1(those who already solved them should know why :wink: ).
A twisty puzzle is not necessarily a geometrical puzzle.
I think abstract twisty puzzles also could exist. All depend on the definition...
You have a much better imagination than me, almost all the new puzzles you come up with are a surprise. With regard to basic twisty puzzles, have you exhausted all face-turning-dodecahedron possibilities? I can see that 1.1.1 - 1.1.7 are all the possibilities for one-cut-per-face but do your puzzles like 1.1.8, 19, 39, 42, etc really exhaust all the combination/hybrid/2-cut puzzles? 1.1.x is my favorite category so I'd love to solve any additional possibilities that exist!

With regard to your 2D puzzles, I agree that 7.1.1 is unique among all your other twisty puzzles. I'd prefer to solve puzzles that have a finite area/volume due to a property of the puzzle rather than an arbitrary cutoff.

For 7.1.x style puzzles, there is another type of move possible -- namely the flip rather than twist. If instead of clicking on a hexagon and having it spin pi/3, it could be picked up into the 3rd dimension, flipped over, and set back down. Much as though you made a twisty puzzle out of flipping playing cards laid out in a grid.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 05, 2010 1:19 am 
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Stefan Schwalbe wrote:
Katten wrote:
Thanks. I worked out a way of easily recognize the pieces quickly. Also might have something to do with the fact that recently I've enjoyed physical puzzle solving, so I easily recognize colors as well
I'm not able to reach your 03:46 on 3.1.8. Also congrats for reaching your 100th gelatinbrain puzzle.
Congratulations indeed. Soon you will overtake me.

I just gave 3.1.8 a few solves and got a 00:50 solve. If i were to give any hints i'd say orientation of the last layer edges is difficult to see... so don't bother looking for it. Pretty sure, due to identical pieces and the fact you just need the blue green edges to be different to each other and the same for the red orange edges, you have a 1 in 4 chance of not needing to perform any algs so just hope for the best and skip the step :lol: I find F2L and the cross very easy and i ignore the edge orientation so oll is super easy so it's just pll that is really more of a struggle than normal so i just did a few solves till i got a T perm (the only pll alg i can remember how to perform quickly on a computer) and got lucky with edge orientation.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 05, 2010 2:44 am 
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bmenrigh wrote:
With regard to basic twisty puzzles, have you exhausted all face-turning-dodecahedron possibilities? I can see that 1.1.1 - 1.1.7 are all the possibilities for one-cut-per-face but do your puzzles like 1.1.8, 19, 39, 42, etc really exhaust all the combination/hybrid/2-cut puzzles? 1.1.x is my favorite category so I'd love to solve any additional possibilities that exist!


I think there are definitely more 2-cut face-turning dodecahedra. Just now I played with Ultimate Magic Cube for a while. I could add arbitrary face cuts (or corner/edge) with any depth. There should be at least tens of possibilities, most of which look pretty messy and complicated because of numerous small pieces. For certain combinations of depths, the cuts intersect on edges or corners, making it less complicated. Here are some screenshots of the puzzles that are "acceptable":

Attachment:
File comment: depths: 69 and 90
69_90.PNG
69_90.PNG [ 14.32 KiB | Viewed 5658 times ]


Attachment:
File comment: depths: 69 and 110
69_110.PNG
69_110.PNG [ 15.63 KiB | Viewed 5658 times ]


Attachment:
File comment: depths: 69 and 137
69_137.PNG
69_137.PNG [ 17.02 KiB | Viewed 5658 times ]


Attachment:
File comment: depths: 85 and 137
85_137.PNG
85_137.PNG [ 16.98 KiB | Viewed 5658 times ]


Attachment:
File comment: depths: 100 and 180
100_180.PNG
100_180.PNG [ 14.35 KiB | Viewed 5658 times ]


Attachment:
File comment: depths: 115 and 153
115_153.PNG
115_153.PNG [ 17.21 KiB | Viewed 5658 times ]


The labels and filenames of these pictures indicate the depth of cuts used in the Ultimate Magic Cube program. These are just some examples and not all possibilities. It may be possible that some of the above puzzles have already been covered by the truncated dodecahedra like 1.1.13 ~ 18.

Well, I'm not requesting GB to add these puzzles, because that would mean too much work for him, (and for me to solve :lol: ).


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 05, 2010 3:56 am 
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Elwyn wrote:
Congratulations indeed. Soon you will overtake me.
Thanks :D I've been having a lot of free time to spend on solving lately.

3.1.8
Elwyn wrote:
If i were to give any hints i'd say orientation of the last layer edges is difficult to see... so don't bother looking for it.
That's what I did as well, but I'm still not adjusted to solving a 3x3x3 disguised as a circle 2x2x2 yet, so it gets confusing for me still. For instants I'd like to find a good way of telling if you need to perform any orientation algorithms of the edges. For computer solves, I always use beginners methods for such puzzles, hence orientation of the edges, permutation of the edges, permutation of the corners and then orientation of the corners. I just like it best that way :lol:
schuma wrote:
I think there are definitely more 2-cut face-turning dodecahedra.
I agree. This picture is posted way back in this thread. This is really the only example I've got. I'm not so creative :lol: My point however, is that with creativity (which is very obvious that Gelatinbrain's got plenty of) I'm certain that schuma is right; there's more doable possibilities.

Not sure this would qualify as "new" puzzles, but there's also a bunch of the 1.1.x puzzles that doesn't have a circle version. For example: 1.1.9/Gigaminx, 1.1.10, 1.1.11. Some of these would be really cool as circle puzzles, but maybe not really a completely new puzzle. If this in some level does count, there's also the option of making a higher order of a puzzle that already exist. For example higher order 1.1.2 --> 1.1.9 + 1.1.10 hybrid.
bmenrigh wrote:
1.1.x is my favorite category so I'd love to solve any additional possibilities that exist!
I'm also getting strangely fond of these beasts. I would think I'd be able to finish most of them, but then there's the super-circle-Pentultimates (1.1.35b/c) :lol:


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 05, 2010 4:15 am 
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Katten wrote:
I agree. This picture is posted way back in this thread. This is really the only example I've got. I'm not so creative :lol: My point however, is that with creativity (which is very obvious that Gelatinbrain's got plenty of) I'm certain that schuma is right; there's more doable possibilities.


Oh yes, what you mentioned is the "4x4" version of megaminx. It is so natural that I actually thought GB had made it :?.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 05, 2010 7:20 am 
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schuma wrote:
I think there are definitely more 2-cut face-turning dodecahedra. Just now I played with Ultimate Magic Cube for a while. I could add arbitrary face cuts (or corner/edge) with any depth. Here are some screenshots of the puzzles that are "acceptable"
Nice! I like the 4th and 5th ones best, especially the 5th (1.1.3 Pyraminx Crystal + 1.1.7 Pentultimate).


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 05, 2010 1:29 pm 
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schuma wrote:
Oh yes, what you mentioned is the "4x4" version of megaminx. It is so natural that I actually thought GB had made it :?.

It's 2.2.10b. 8-)

Yes, there are more possible 4~5 layer dodecahedra. The problem is they contain too many minuscule pieces. Schuma's examples are really at the limit of acceptable. But before adding them, I want to find an ideal cut and shape in which all pieces are more or less proportionable.

You can make a new puzzles also by simply adding layers.
But I will not add puzzles containing more than 7 layers(pétaminx,8x8x8 cube...).
I will have to extend the interface to support deeper layers. And I don't think that adding layers create an essentially new challenge to solvers. Rather, it makes the puzzle more tedious and time-consuming. Many will agree that the pentultimate is much more challenging than the téraminx.

I rather want to discover simple puzzles with limited pieces, but require a new way of thinking to solve.
My recent puzzles, slide cubes(3.10.*), differential circle cubes(3.1.27~30), elastic cubes(3.7.6~8),s are along this line. Oscar's recent Arrow Planet too, hints me a whole unexplored territory.
Some would say they are no longer twisty puzzles. But in my view, they are logical and quite natural extentions of Rubik's. Along with traditional twisty puzzles they deserve a special place in methematics. Beyond the group theory and the graph theory,
someone should create a twisty puzzle theory(but clearly I'm not qualified :oops:).

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 05, 2010 3:49 pm 
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schuma wrote:
ortwin wrote:
Gelatinbrain my suggestion for a further puzzle is a quite obvious one- at least for me.
3.1.3 (4x4x4) combined with
3.2.1 (skewb) with
3.2.4 (dino) with
3.3.1 (helicopter) and with
3.3.7 (little chop)

Four layers in faces, edges and vertices.

You have some puzzles that are close, but not quite what I mean: 3.7.2 , 3.7.5 ...

Or did I miss something?


GB has added such a puzzle: 3.7.9. What a massive puzzle!


hm, what do I have to do to see it? For me 3.7.8 is still followed by 4.1.1.

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Last edited by ortwin on Sun Dec 19, 2010 6:30 am, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 05, 2010 5:10 pm 
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ortwin wrote:

hm, what do I have to do to see it? For me 3.7.8 is still followed by 4.1.1.


I can find it using the following way: Open any puzzle and go to the File menu on the top left corner -> New -> Cubes -> mixed -> the last one is 3.7.9 (it doesn't have a thumbnail). There might be some java caching issue so that you cannot even find it this way...


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Dec 06, 2010 10:20 am 
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schuma wrote:
ortwin wrote:

hm, what do I have to do to see it? For me 3.7.8 is still followed by 4.1.1.


I can find it using the following way: Open any puzzle and go to the File menu on the top left corner -> New -> Cubes -> mixed -> the last one is 3.7.9 (it doesn't have a thumbnail). There might be some java caching issue so that you cannot even find it this way...



I looked for it on this page. That is what my cited comment above relates to. Now I downloaded the Windows app version from that page, the "mixed" list ends for me with 3.6.5 , so obviously I am seeing something different from you.
I did empty everyrhing in the java cache. I tried on two different computers. Any suggestions what to try next?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Dec 06, 2010 4:25 pm 
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ortwin wrote:
I looked for it on this page. That is what my cited comment above relates to. Now I downloaded the Windows app version from that page, the "mixed" list ends for me with 3.6.5 , so obviously I am seeing something different from you.
I did empty everyrhing in the java cache. I tried on two different computers. Any suggestions what to try next?

The downloadable version is not yet updated. You can play new puzzles only online.
Click any picture on the main page(3.7.9 is not on the list).
Then click the button labeld "file" on the upper left of the applet.
From the menu, choose [cube]->[mixed]->[3.7.9].
If you don't see it on the menu, then clear your browser's cache and retry (relaunch the browser).

I will update the downloadable version once more until the end of the year, maybe. But I don't have time now, my excuses...

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Dec 06, 2010 4:45 pm 
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1.1.35/Circle Pentultimate
Julian wrote:
First make a (3,1) algo where the 3 moves use two non-adjacent faces, pushing one center and two corners into another half, and that half is twisted on the 4th and 8th moves. After the 8 moves, look carefully at another half, which has remained the same apart from one corner and two circle pieces. With an extra move, the corner and one of the circle pieces is moved out of that half, leaving just a swapped circle piece in the half: [inverse of extra move] + (3,1) + [extra move] = 10 moves to isolate a single swapped circle piece.
I finally sat down looking for this algo, and I believe I found it, though I used a (4,1) + (extra move) to isolate that single swapped circle piece. But can't be too much different from yours, Julian? Anyways here it is:

A', J, A, J', D', J, A', J', A, D,
I',
C', F, C, F', D, F, C', F', C, D',
I,

Time to get ride of that 10 000 move solve!

PS: if anyone thinks I should write algos like this with invisible ink instead so that you get to get a chance at figuring it out for yourself first, please PM me telling me exactly how to do that :lol:


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Dec 07, 2010 3:43 pm 
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gelatinbrain wrote:
The downloadable version is not yet updated. You can play new puzzles only online.
Click any picture on the main page(3.7.9 is not on the list).
Then click the button labeld "file" on the upper left of the applet.
From the menu, choose [cube]->[mixed]->[3.7.9].
If you don't see it on the menu, then clear your browser's cache and retry (relaunch the browser).

I will update the downloadable version once more until the end of the year, maybe. But I don't have time now, my excuses...


I can see it now! Thank you all for the hints, it took three times the same answer from different persons until stupid me got it. Additionally I had to find out that my ad-blocker got temporarly in my way.

I really like it, I have to play a while to find out how hard it is.

But, as soon as a wish fullfilled, it fathers new ones:

Gelatinbrain: In the section "3.7 Twist around faces,vertices or edges" there is 3.7.2 where you have two layers regarding faces, verices and edges. In 3.7.9 there are now four layers in all three.... whatever you call it.
So what is still needed in this little symmetric series is three layers in faces,vertices and edges.
That would be a combination of a
3x3x3 (3.1.2)
dino cube (3.2.4) and
helicopter cube (3.3.1)

Is there a chance to get such a cube?

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Dec 07, 2010 3:49 pm 
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Katten wrote:
I finally sat down looking for this algo, and I believe I found it, though I used a (4,1) + (extra move) to isolate that single swapped circle piece. But can't be too much different from yours, Julian? Anyways here it is:

A', J, A, J', D', J, A', J', A, D,
I',
C', F, C, F', D, F, C', F', C, D',
I,

Time to get ride of that 10 000 move solve!

PS: if anyone thinks I should write algos like this with invisible ink instead so that you get to get a chance at figuring it out for yourself first, please PM me telling me exactly how to do that

Now I have an algorithm too. For me it is ok to read the moves. :D
gelatinbrain wrote:
I rather want to discover simple puzzles with limited pieces, but require a new way of thinking to solve.
These new puzzles are fine.
schuma wrote:
I think there are definitely more 2-cut face-turning dodecahedra. Just now I played with Ultimate Magic Cube for a while. I could add arbitrary face cuts (or corner/edge) with any depth. There should be at least tens of possibilities, most of which look pretty messy and complicated because of numerous small pieces. For certain combinations of depths, the cuts intersect on edges or corners, making it less complicated. Here are some screenshots of the puzzles that are "acceptable":

Hi schuma, I want to play with Ultimate Magic Cube too. I get two warnings and then it terminates:
Attachment:
umc1.png
umc1.png [ 8.75 KiB | Viewed 5434 times ]
Attachment:
umc2.png
umc2.png [ 7.67 KiB | Viewed 5434 times ]
I have installed direct x 9. Can you help me?
gelatinbrain wrote:
I don't like these things either. I don't want to mess up my code by indiscriminately adding everything. It's better to fix a border. First I'd like to exhaust most basic twisty puzzles and then classify them.
I don't have yet my own clear definition of twisty puzzles, neither a good method to classify them. But most basic twisty puzzles are certainly symmetrical ones.
They are far more numerous than I first imagined.
Nobody can add everything. I think you are absolutely right to fix a border. I believe, it is possible, to create a puzzle-systematic. Maybe pick one of the 7 symmetric direction sets and discover all piecetypes that you can get with a single cut. I came more and more to the conclusion, that a twisty puzzle is a combination (or composition) of piecetypes. That helps me also solving. A puzzle is a combination of aspects: piecetype 1 permutation, piecetype 1 orientation, piecetype 2 permutation, piecetype 2 orientation and so on. With the puzzle-layout you can decide, wich aspects you want to show, and wich not. Infinite! On the bigger sets (for example 30 dodecahedron edges) even the single cut puzzles are too much.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Dec 07, 2010 4:15 pm 
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Katten wrote:
1.1.35/Circle Pentultimate

I finally sat down looking for this algo, and I believe I found it, though I used a (4,1) + (extra move) to isolate that single swapped circle piece. But can't be too much different from yours, Julian?
Somewhat similar, yes. Having 2 of the 3 pieces on the same face can be useful some of the time but probably makes setups trickier and longer the rest of the time. As a supplement for your re-solve, if you like, here is my (10,1) pure cycle in invisible ink, which affects pieces on 3 different faces: (A (C F C', G) A', I)

To write text in invisible ink, highlight the text and click a font color over to the right. Then, if your post is going to be gray because it follows a white post, edit the color code to EEEEEE; whereas if your post is going to be white because it follows a gray post, edit the color code to FFFFFF.


Last edited by Julian on Tue Dec 07, 2010 5:49 pm, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Dec 07, 2010 4:58 pm 
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3.7.9 (4x4x4 + Dino Cube + Skewb + Helicopter Cube + Little Chop)

Solution Outline

The puzzle has 4 piece types, each with 48 pieces in 2 distinct subgroups of 24 (which I call left-handed and right-handed). It is sometimes quicker to cycle a piece type in pairs first to solve most of one subgroup quickly, then switch to purer algos to cycle individual pieces of one subgroup without affecting the pieces in the other.
Attachment:
GB 3-7-9.png
GB 3-7-9.png [ 26.52 KiB | Viewed 5493 times ]
1 - Blockbuild face by face intuitively, including 4x4x4 center-solving techniques, up to the last few pieces of the last 3 adjacent faces, then finish with (1,1) commutators.

2 - Use 3x3x3 and 4x4x4 edge techniques to quickly place as many pieces correctly as possible, then finish by cycling with (3,1) commutators.

3 - Cycle first in pairs (3,1), then singly (4,1).

4 - Cycle first in pairs (1,1), then singly (4,1).


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Dec 07, 2010 6:37 pm 
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Stefan Schwalbe wrote:
I came more and more to the conclusion, that a twisty puzzle is a combination (or composition) of piecetypes. That helps me also solving. A puzzle is a combination of aspects: piecetype 1 permutation, piecetype 1 orientation, piecetype 2 permutation, piecetype 2 orientation and so on.

I agree with you on basis. But more I discover new puzzles, more they makes me confused.
Anyway, the definition and classification of puzzles should be based on their abstractions(graphical stracture, group configuration, piece attributes, etc) and not on their physical or geometrical aspect. It is not that easy even under very limited conditions...

Julian wrote:
To write text in invisible ink, highlight the text and click a font color over to the right. Then, if your post is going to be gray because it follows a white post, edit the color code to EEEEEE; whereas if your post is going to be white because it follows a gray post, edit the color code to FFFFFF.

What happens if someone deletes his post and the paritity of all subseqent posts flips? :lol:

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Dec 08, 2010 12:44 pm 
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Stefan Schwalbe wrote:
I came more and more to the conclusion, that a twisty puzzle is a combination (or composition) of piecetypes. That helps me also solving. A puzzle is a combination of aspects: piecetype 1 permutation, piecetype 1 orientation, piecetype 2 permutation, piecetype 2 orientation and so on.
gelatinbrain wrote:
I agree with you on basis. But more I discover new puzzles, more they makes me confused.
Anyway, the definition and classification of puzzles should be based on their abstractions(graphical stracture, group configuration, piece attributes, etc) and not on their physical or geometrical aspect. It is not that easy even under very limited conditions...
Great minds think alike:
viewtopic.php?p=190396#p190396
Based on what Stefan outlined there are 18 derivates of the 3x3x3, including the 1x1x1. Examples for all of them are shown here: viewtopic.php?f=14&t=17517
Based on what Stefan outlined above there are 972 diferent faceturning dodecahedrons, including the (dodecahedral) 1x1x1. Even more variants are possible, if the pieces from the circleMegaminx's are considered.
EDIT: Corrected links


Last edited by Andreas Nortmann on Fri Dec 10, 2010 10:51 am, edited 1 time in total.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Dec 08, 2010 1:50 pm 
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gelatinbrain wrote:
What happens if someone deletes his post and the paritity of all subseqent posts flips? :lol:
Fortunately that can't happen, because you can't delete a post if other people have posted after you in the same thread. However, if people have added posts to the same thread while you are writing your post, you do need to count the extra posts and toggle the gray and white correctly!


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Dec 08, 2010 3:18 pm 
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Julian wrote:
Having 2 of the 3 pieces on the same face can be useful some of the time but probably makes setups trickier and longer the rest of the time.
Actually, the set-ups were easier than I thought. I had more trouble setting up the corners than the circle pieces. My re-solve using this routine went pretty well I reckon. I also went ahead and solved 1.1.35b and c (as a side note; 1.1.35c is probably my favorite puzzle by appearance). If I ever want to try a solve for fewest moves, I'll certainly try out your routine, thanks :D


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Dec 08, 2010 7:23 pm 
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Andreas Nortmann wrote:
Based on what Stefan outlined there are 18 derivates of the 3x3x3, including the 1x1x1. Examples for all of them are shown here: viewtopic.php?f=14&t=17517

Thank you for the links. Adding to your collection, I think there are also cubes with duplicate pieces.
So called "Shepherd's Cube" is an example. 2x2x2 Shepherd Cube consists of
2 non-oriented pieces and 6 oriented pieces, and each divided in two mirror groups.
It's functionally equivalent to my maze 2x2x2(3.1.1b).
Attachment:
arrow2.gif
arrow2.gif [ 7.22 KiB | Viewed 5347 times ]

Attachment:
arrow3.gif
arrow3.gif [ 7.32 KiB | Viewed 5347 times ]

The following variation consists of two sets(2 non-oriented + 6 oriented) of identical pieces.
Attachment:
arrow1.gif
arrow1.gif [ 7.09 KiB | Viewed 5347 times ]

Attachment:
arrow4.gif
arrow4.gif [ 4.1 KiB | Viewed 5347 times ]

Even for the 2x2x2, I don't know how many "functionally different" puzzles, but I stop here. It will be far beyond the scope of this thread...

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Dec 09, 2010 1:12 pm 
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gelatinbrain wrote:
Even for the 2x2x2, I don't know how many "functionally different" puzzles, , but I stop here. It will be far beyond the scope of this thread...
Okay. This thread is about solving.
But in case of the 2x2x2 there are 746.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Dec 09, 2010 3:32 pm 
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Andreas Nortmann wrote:
Great minds think alike:
viewtopic.php?f=1&t=15614&p=190396
Based on what Stefan outlined there are 18 derivates of the 3x3x3, including the 1x1x1. Examples for all of them are shown here: viewtopic.php?f=14&t=17517
Based on what Stefan outlined above there are 972 diferent faceturning dodecahedrons, including the (dodecahedral) 1x1x1. Even more variants are possible, if the pieces from the circleMegaminx's are considered.
Thank you, Andreas. Very interesting links. I could even play with orientation-only pieces i.e. a set of identical pieces, wich show orientation. This discussian is maybe worth a new thread. I have found 17 piecetypes on the singlecut icosahedron set. I posted that before on this thread.
gelatinbrain wrote:
I agree with you on basis. But more I discover new puzzles, more they makes me confused.
Yes it's a barrel without ground.
Julian wrote:
3.7.9 (4x4x4 + Dino Cube + Skewb + Helicopter Cube + Little Chop)

Solution Outline
...
Beautiful solution, Julian!
gelatinbrain wrote:
My 2D puzzles 7.1.2 & 7.1.3 should also classified into this group, but not 7.1.1(those who already solved them should know why ).
Nethertheless, fun to play with 7.1.1


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Dec 09, 2010 6:29 pm 
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Stefan Schwalbe wrote:
I could even play with orientation-only pieces i.e. a set of identical pieces, wich show orientation.

As far as I know, 2-color 2x2x2(a pair of opposite faces and the rest painted in different colors), is the only physical puzzle consisting of only one set of identical and oriented pieces. This can be harder than a regular 2x2x2.
In all my puzzles, I think only 3.9.1, 3.9.1b and 3.7.6b belong to this category.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Dec 10, 2010 1:41 am 
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Stefan Schwalbe wrote:
I have found 17 piecetypes on the singlecut icosahedron set. I posted that before on this thread.


Hi Stefan,

Today I made an illustration of a single-cut octahedron with internal pieces and posted it here. It's partly inspired by your work. I think such an illustration would be very interesting and very complicated for an icosahedron. But one can find all the pieces that you have classified in it. And, it would be very cool if anyone makes a program like this. It should be possible to solve if there is an option to make outer layers transparent. I guess the interface will be like that of MC4D. I need to learn a lot in order to make such a program by myself.

-- schuma


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Dec 10, 2010 11:51 am 
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Stefan Schwalbe wrote:
This discussian is maybe worth a new thread.
True.
viewtopic.php?f=1&t=19749

@Schuma: I answer to your post in that thread too.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Fri Dec 10, 2010 5:33 pm 
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gelatinbrain wrote:
Stefan Schwalbe wrote:
I could even play with orientation-only pieces i.e. a set of identical pieces, wich show orientation.

As far as I know, 2-color 2x2x2(a pair of opposite faces and the rest painted in different colors), is the only physical puzzle consisting of only one set of identical and oriented pieces. This can be harder than a regular 2x2x2.
In all my puzzles, I think only 3.9.1, 3.9.1b and 3.7.6b belong to this category.

I mean, two sets is also okay like your 3.11.1 for instance. :D

Hi schuma, I have answerd in the new thread.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Dec 11, 2010 6:34 am 
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schuma wrote:
Today I made an illustration of a single-cut octahedron with internal pieces and posted it here.


Added a new circle FTO (4.1.16) with bigger circles intersecting each other.
Image
This is the only face turning octahedron with the core piece exposed. By adding small circles to this, you can make a puzzle including all pieces in your picture(but inevitably other minuscule pieces too :( ).

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Dec 11, 2010 8:35 am 
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gelatinbrain wrote:
Added a new circle FTO (4.1.16) with bigger circles intersecting each other.
Thanks!

Please would it be possible for you to add a puzzle to 2.1.x? The one shown below is the same depth of cut as 1.2.6, cutting the puzzle into 3 equally thick layers in each axis. It has far fewer pieces than 2.1.4 because the deeper cuts eliminate 7 center pieces per face, but it introduces some new edges.
Attachment:
UMC Icosa F120.png
UMC Icosa F120.png [ 13.76 KiB | Viewed 4925 times ]


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Dec 11, 2010 1:20 pm 
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gelatinbrain wrote:
Added a new circle FTO (4.1.16) with bigger circles intersecting each other.
Image
This is the only face turning octahedron with the core piece exposed. By adding small circles to this, you can make a puzzle including all pieces in your picture(but inevitably other minuscule pieces too :( ).


Thanks. I'm also thinking of how to make circle puzzles to include all the internal pieces, but haven't found the answer. Apparently you have find it. The difficulty I had is, I don't know how to include the inner face center (from 4.1.3) and the outer face center (from 4.1.1) simultaneously. I'll look into your 4.1.16.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sat Dec 11, 2010 2:58 pm 
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schuma wrote:
gelatinbrain wrote:
Added a new circle FTO (4.1.16) with bigger circles intersecting each other.
Image
This is the only face turning octahedron with the core piece exposed. By adding small circles to this, you can make a puzzle including all pieces in your picture(but inevitably other minuscule pieces too :( ).


Thanks. I'm also thinking of how to make circle puzzles to include all the internal pieces, but haven't found the answer. Apparently you have find it. The difficulty I had is, I don't know how to include the inner face center (from 4.1.3) and the outer face center (from 4.1.1) simultaneously. I'll look into your 4.1.16.

I've been thinking about how to expose some central pieces with circle cuts too and I think if you give the puzzle faces a really strange curve (such as concave) you can get down into some of those central pieces. Combining that with your ring circle cuts might do the trick.

Basically I'm thinking of
Attachment:
Inverted2x2x2.jpg
Inverted2x2x2.jpg [ 17.92 KiB | Viewed 4903 times ]
+
Attachment:
hexa_f32.gif
hexa_f32.gif [ 2.81 KiB | Viewed 4903 times ]


I haven't worked idea out in enough detail to see where it leads though...

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 12, 2010 4:15 pm 
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gelatinbrain wrote:
By adding small circles to this, you can make a puzzle including all pieces in your picture(but inevitably other minuscule pieces too :( ).


I see your new puzzle 4.1.16 that has two circles. I am convinced that it includes all pieces in the octahedron multicube (aka multi-HC2). It distinguishes the triangle pieces in FTO (4.1.2), making it slightly harder. It even includes one more type of circle pieces that is not there in the multicube. I really enjoy solving it. Thanks.

By the way, Brandon solved another multicube -- the dodecahedron, by switching between different GB puzzles. Link. Since making a true multi-dodecahedron using circles would be too complicated, this is a clever roundabout way.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 12, 2010 5:01 pm 
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schuma wrote:
gelatinbrain wrote:
I see your new puzzle 4.1.16 that has two circles. I am convinced that it includes all pieces in the octahedron multicube (aka multi-HC2)..

This puzzle contains all pieces of 4.1.4 and the visible core piece, but not the centers of 4.1.3 as you suggested.
The only way I can think of to contain two set of centers in one puzzle is making a peephole on the center ...

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 12, 2010 6:00 pm 
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gelatinbrain wrote:
This puzzle contains all pieces of 4.1.4 and the visible core piece, but not the centers of 4.1.3 as you suggested.
The only way I can think of to contain two set of centers in one puzzle is making a peephole on the center ...


I believe it has. Here is my analysis:
Attachment:
4116.PNG
4116.PNG [ 23.5 KiB | Viewed 4756 times ]

1. The three pieces with label 1 form a group that always move together (somebody call it a virtual piece). It is the center of 4.1.3 on the red face, because it never moves but can be rotated by and only by the red face.

2. The piece with label 2 never moves, It belongs to the core.

3. The group of two pieces with label 3 is an edge piece on 4.1.3. It can be rotated by two adjacent faces.

4. The two pieces with label 4 is virtually connected. It is the triangle piece of 4.1.2. But in 4.1.2, three triangles on each face are identical. However, in 4.1.16, they are differentiated by the small crescent piece.

5. The center piece of 4.1.1 or 4.1.4.

6. Corner piece.

7. The two pieces with label 7 is virtually connected. It is a new piece, which doesn't belong to any puzzle from 4.1.1 to 4.1.4. It can be rotated by the left front face and right front face. No piece in 4.1.1 ~ 4.1.4 has such a turning property, right?


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Sun Dec 12, 2010 6:54 pm 
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:idea: Just before seeing your latest post, schuma, I noticed that, solving-wise, 4.1.16 = 4.1.11* + 4.1.4 centers, with the overall orientation set by the overlaps of the bigger circles. I'll try solving 4.1.16 that way tomorrow. It is a fun puzzle!

* Except the number 4 pieces in your diagram are 24 unique pairs instead of 8 sets of 3 identical pieces, as you point out. Nice analysis!

Gelatinbrain -- Thanks for adding 2.1.7. I think we are now very close to a full set of every possible "sensible"/acceptable puzzle made from a Platonic solid with a single cut around each face, vertex, or edge. Of course this is subjective! For example, I think it would be nice to have a shallower cut Dino Cube with fixed centers and spinning corners, to add a variation and slight extra difficulty to this very easy and quick puzzle. :) But on the other hand, I would rather not see a shallower-cut 2.1.1 with fixed centers, because I don't see the point. :| Other possibilities not already included or mentioned all seem to have tiny pieces, and/or a huge number of pieces. :?


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Dec 13, 2010 5:59 pm 
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Thanks Gelatinbrain for adding 2.1.7, and thanks to Julian for asking gelatinbrain to make it.
It's DC2 [F3,E12,X18,T21][F3,E12] in Andreas Nortmann's marvelous classification system. :shock: (I hope that is correct.)
solution outline:
Attachment:
2.1.7.png
2.1.7.png [ 23.62 KiB | Viewed 4715 times ]

I (F3) corners: no comment
II (X18) corner-faces: (3,1)
III (T21) edge-corner: (3,1)
IV (E12) edge: (1,1)
I solved always one piece at once, learning the setups.
Hi Brandon, congrats. for solving the multi-dodecahedron.
The 4.1.16 seems to look harder than it is.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Dec 13, 2010 6:10 pm 
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Stefan, can you see 1.3.12?

If you do, can you please post a picture of it?


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Dec 13, 2010 6:37 pm 
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Sharon wrote:
Stefan, can you see 1.3.12?
If you do, can you please post a picture of it?
Sharon

1.3.12 = 1.1.5 + 1.2.6. I will upload the gif later.

Schuma, you are right. The piece type 2 is the center of 4.1.3, but oriented(super-stickered). That's why I missed it.
The piece 7 is indeed a strange entity. As I see, it doesn't belong to any of known piece types(face,corner,edge,inner). It doesn't exist in any other of the 4.1.x family, and can not exist in planar cut FTO.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Dec 13, 2010 8:00 pm 
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Gelatinbrain, thanks so much for these new puzzles! Your continued creativity, insight, and hard work is always appreciated!
gelatinbrain wrote:
Schuma, you are right. The piece type 2 is the center of 4.1.3, but oriented(super-stickered). That's why I missed it.
The piece 7 is indeed a strange entity. As I see, it doesn't belong to any of known piece types(face,corner,edge,inner). It doesn't exist in any other of the 4.1.x family, and can not exist in planar cut FTO.
I haven't had time to twist any of the new Circle FTOs but isn't piece 7 the same strange half-corner piece from your original Circle FTO (4.1.11)?

I couldn't figure out what that piece was either when I solved 4.1.11. I ended up thinking of it as one part of a pair that together formed an inner-corner. That is, if the corner is a + piece than it also has a - and | that overlap right below the corner.

This extra piece made 4.1.11 conceptually quite hard for me.

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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Mon Dec 13, 2010 9:09 pm 
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bmenrigh wrote:
I haven't had time to twist any of the new Circle FTOs but isn't piece 7 the same strange half-corner piece from your original Circle FTO (4.1.11)?

I couldn't figure out what that piece was either when I solved 4.1.11. I ended up thinking of it as one part of a pair that together formed an inner-corner. That is, if the corner is a + piece than it also has a - and | that overlap right below the corner.

This extra piece made 4.1.11 conceptually quite hard for me.


You are right about number 7 pieces appeared in 4.1.11. As Julian said, 4.1.16 = 4.1.11 + 4.1.4 centers. But when I solved 4.1.16, I forgot about 4.1.11 and thus forgot to make connections to it. I think your understanding of - and | is correct. They are crossing each other under an "outer" corner.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Dec 14, 2010 4:08 pm 
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Stefan Schwalbe wrote:
It's DC2 [F3,E12,X18,T21][F3,E12] in Andreas Nortmann's marvelous classification system. :shock: (I hope that is correct.)
It is correct.
gelatinbrain wrote:
[Regarding 4.1.16]
The piece 7 is indeed a strange entity. As I see, it doesn't belong to any of known piece types(face,corner,edge,inner). It doesn't exist in any other of the 4.1.x family, and can not exist in planar cut FTO.
Correct.
Piece 7 is one of the three types of ZPH (Pieces with zero volume under all configurations of equidistant cuts which can still act as holding point; formerly known as virtual pieces) which exist in HC2.
So the signature could be: HC2[O, C1, C4, F3, E3, X9, VE3][C1, F3, VE3]
I want to mention that these ZPH's aren't yet fully included in my system.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Dec 14, 2010 5:18 pm 
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Sharon wrote:
Stefan, can you see 1.3.12?
If you do, can you please post a picture of it?
Sharon

Yes here is the picture of 1.3.12
Attachment:
1.3.12.png
1.3.12.png [ 42.22 KiB | Viewed 4646 times ]

The lines I have added. It can turn faces and corners. I didn't know that - it looks nice.
gelatinbrain wrote:
1.3.12 = 1.1.5 + 1.2.6. I will upload the gif later.
Julian wrote:
But on the other hand, I would rather not see a shallower-cut 2.1.1 with fixed centers, because I don't see the point. Other possibilities not already included or mentioned all seem to have tiny pieces, and/or a huge number of pieces.
I'm not sure. Maybe there are more nice singlecut faceturning icosahedrons, wich would make a good addition. Why not the easier shallower cut ones. On other solids for instance the cube we have also everything. At least, the singlecut puzzles should be complete. I'm about asking gelatinbrain for it, but I don't know how they exactly look. I have only my sphere-applet images. Also I have to solve all the other puzzles. Maybe sometime later.

Andreas Nortmann wrote:
So the signature could be: HC2[O, C1, C4, F3, E3, X9, VE3][C1, F3, VE3]
I'm interested :D .
I have allowed myself to make this signature visible:
Attachment:
4.1.16.png
4.1.16.png [ 35.36 KiB | Viewed 4638 times ]


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Tue Dec 14, 2010 9:02 pm 
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Stefan Schwalbe wrote:
Julian wrote:
But on the other hand, I would rather not see a shallower-cut 2.1.1 with fixed centers, because I don't see the point. Other possibilities not already included or mentioned all seem to have tiny pieces, and/or a huge number of pieces.
I'm not sure. Maybe there are more nice singlecut faceturning icosahedrons, wich would make a good addition. Why not the easier shallower cut ones. On other solids for instance the cube we have also everything. At least, the singlecut puzzles should be complete.
You are right about the face-turning icosahedra! I have just been on a puzzle hunt with UMC (the error you posted earlier indicates that your graphics card is not capable of running UMC, I think, unfortunately). There are 14 distinct possible single cut FTI puzzles, 6 of which have 290+ pieces so I suggest are out of bounds. The other 8 are, in order of cuts getting deeper:

Shallow-cut 2.1.1 with stationary centers
2.1.1
2.1.2
2.1.3
The puzzle shown below, which has the same number of pieces (242) as 2.1.4
2.1.4
2.1.7
2.1.5

Attachment:
UMC Icosa F78.png
UMC Icosa F78.png [ 12.24 KiB | Viewed 4627 times ]

Regarding possible complete sets of single cut puzzles, here are some scary examples...

There are 18 possible single cut 1.2.x puzzles:
Shallow 1.2.1 with corners exposed, 1.2.1, 1.2.1+1.2.2 hybrid, 1.2.2, 1.2.2+1.2.3 hybrid, 1.2.3, and so on.

There are 41 possible single cut 1.4.x puzzles: 1.4.1, 1.4.1+1.4.4 hybrid, 1.4.4, 1.4.4+1.4.5 hybrid, 1.4.5, 1.4.5+1.4.2 hybrid, 1.4.2, several crazy puzzles with far too many pieces between 1.4.2 and 1.4.6, and so on. 1.4.6 is the only puzzle between 1.4.2 and the Big Chop with fewer than 500 pieces! Here is a nice animation made by Carl/wwwmwww showing the 41 puzzles one after another.

Edit: As the above examples show, even single cut puzzles can get too crazy to have a full set. While it's worthwhile looking around for any extra single cut puzzles to request, I doubt that there are many left to find, because GB has already done an excellent job of looking through the possibilities and including the "acceptable" ones.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Dec 15, 2010 3:29 pm 
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Hello gelatinbrain, can you please add the puzzle on the picture of Julians last post? I would like to play with it. And maybe one or two shallow cut icosahedra:
Attachment:
ico265.jpg
ico265.jpg [ 95.53 KiB | Viewed 4594 times ]
Attachment:
ico238.jpg
ico238.jpg [ 99.8 KiB | Viewed 4594 times ]
Thank you very much for everything! :?
Hi Julian. good job!


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Wed Dec 15, 2010 3:59 pm 
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Stefan, although you can make the two shallow cuts on a sphere, it seems like you cannot make them on an icosahedron using planar cuts. According to UMC, the extremely shallow planar cut on an icosahedron results in 2.1.1 + face centers. The first model you proposed can be made on a dodecahedron twisting around corners though. It's exactly 1.2.1. For the second model, I don't know on which polyhedron can one make it.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Dec 16, 2010 3:06 pm 
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schuma wrote:
Stefan, although you can make the two shallow cuts on a sphere, it seems like you cannot make them on an icosahedron using planar cuts. According to UMC, the extremely shallow planar cut on an icosahedron results in 2.1.1 + face centers. The first model you proposed can be made on a dodecahedron twisting around corners though. It's exactly 1.2.1. For the second model, I don't know on which polyhedron can one make it.

Ah yes. With planar cuts not possible.
Attachment:
Kegelschnitt.png
Kegelschnitt.png [ 4.37 KiB | Viewed 4551 times ]
Maybe with cone-cuts. Are such cuts possible ?
Julian wrote:
There are 41 possible single cut 1.4.x puzzles: 1.4.1, 1.4.1+1.4.4 hybrid, 1.4.4, 1.4.4+1.4.5 hybrid, 1.4.5, 1.4.5+1.4.2 hybrid, 1.4.2, several crazy puzzles with far too many pieces between 1.4.2 and 1.4.6, and so on. 1.4.6 is the only puzzle between 1.4.2 and the Big Chop with fewer than 500 pieces! Here is a nice animation made by Carl/wwwmwww showing the 41 puzzles one after another.

Edit: As the above examples show, even single cut puzzles can get too crazy to have a full set.
...
I agree a bit, after seeing the linked page with the edgeturning dodecahedron.


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Dec 16, 2010 7:42 pm 
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New icosa face turning puzzles added:

2.1.8 = Circle 2.1.7
2.1.9 = Slice depth between 2.1.3 and 2.1.4

Thanks GB!


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 Post subject: Re: Gelatin Brain's Applet Solutions Discussion Thread
PostPosted: Thu Dec 16, 2010 8:11 pm 
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Joined: Thu Jul 23, 2009 5:06 pm
Location: Berkeley, CA, USA
Actually GB added three face-turning icosahedra. The third is: 2.1.0 ! This one is the second model proposed by Stefan, minus the center pieces.


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