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Brandon Enright

Post subject: How to solve the Rex / Bauhinia Dodecahedron Posted: Thu Dec 06, 2012 4:09 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

Konrad wrote: rline wrote: ...So Konrad, I take it by this that you're saying it will be quite a challenging solve? Will you be using commutators for most things? Yes to both questions (probably more tedious than really hard, but very easy to screw it up), but, please [my moderator self is watching me ], not more about solving in this thread. When the time comes, we can start a topic in the Solving Forum. It won't be so bad to solve. Unjumbling is straightforward. Once it is in its doctrinaire state you can solve the "Rex Dodecahedron Edges" topdown. I'd suggest that as you solve it topdown you also cycle in the large petal pieces with [1,1] commutators. Then I'd solve the center pentagons with [3,1] commutators. There are a lot of easy variations for this but [AFB', ACD, AFB, FJI, AFB', ACD', AFB, FJI'] is one example. Up to this point the puzzle is very easy but the remaining 60 small triangles left are a bit trickier. There is a [5,1] or [3,3] commutator to cycle them. There is some variation to this so you can play with the structure of the commutator to find one that works nicely for you. Here is one example [KDG, EDK', EJF, EDK, KDG', DCG', KDG, EDK', EJF', EDK, KDG', DCG] You can translate these sequences from GB's notation to Konrad's with http://www.brandonenright.net/cgibin/gb_util.pl (EDIT: notation translation not working right now. I'll troubleshoot it when I have the chance.) [Moderator: I have moved this post from this topic to a new topic in the Solving Forum] EDIT: fixed center pentagon 3cycle sequence.
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Last edited by Brandon Enright on Tue Dec 11, 2012 11:17 am, edited 1 time in total.


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Konrad

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Thu Dec 06, 2012 4:45 pm 

Joined: Thu Sep 17, 2009 6:07 am Location: Germany, Bavaria

My approach is pretty much identical to Brandon's outline. I have not scrambled the puzzle yet, but looked for commutators for the different piece types. I have not yet found a sufficiently short sequence for the little triangles. In my first cramble / solve, I will use ordinary, non jumbling moves only. Can it be possible that jumbling creates a new state of the puzzle and it cannot be solved by doctrinaire moves? (Like changing orbits on the Helicopter Cube) Regarding: TP Dodecahedron notation (Your nice sequence utility calls it Konrad's notation, but others have contributed as well) covers Face Turning Dodecahedra. Please have a look here
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Brandon Enright

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Thu Dec 06, 2012 4:55 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

Konrad wrote: Can it be possible that jumbling creates a new state of the puzzle and it cannot be solved by doctrinaire moves? (Like changing orbits on the Helicopter Cube) Nope, jumbling doesn't cause any unexpected problems on this puzzle. The groups of pieces that jumble (see here and here) stay together nicely and you can't separate the pieces once jumbled. This makes unjumbling quite easy. You just find two jumbled groups and unjumble them in pairs.
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rline

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Thu Dec 06, 2012 5:25 pm 

Joined: Mon Feb 28, 2011 4:54 am


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Doug Roth

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Thu Dec 06, 2012 5:56 pm 

Joined: Sun May 29, 2011 2:56 pm Location: New York


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Konrad

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Thu Dec 06, 2012 6:02 pm 

Joined: Thu Sep 17, 2009 6:07 am Location: Germany, Bavaria

Doug Roth wrote: rline wrote: Brandon, which gelatinbrain are you using for this? 2.1.1? That would seem like the logical choice... Doug I did not see anything closer. The Rex Dodecahedron is quite a bit easier than 2.1.1, because there is no orientation for the "corners" and you have got five identical triangles and petals of each colour.
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rline

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Thu Dec 06, 2012 7:11 pm 

Joined: Mon Feb 28, 2011 4:54 am


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Brandon Enright

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Thu Dec 06, 2012 9:09 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

Konrad wrote: Doug Roth wrote: rline wrote: Brandon, which gelatinbrain are you using for this? 2.1.1? That would seem like the logical choice... Doug I did not see anything closer. The Rex Dodecahedron is quite a bit easier than 2.1.1, because there is no orientation for the "corners" and you have got five identical triangles and petals of each colour. Actually I was focusing on 1.2.3 (The Pentagram) since it has the same color scheme as the Rex Dodecahedron. It has corners and is missing edges. You can just ignore the corners and if you want to see the effect of routines on edges you can use 1.2.1 or 1.2.2. It's imperfect but IMO it's better than the totally different color scheme offered by 2.1.1.
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Brandon Enright

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Thu Dec 06, 2012 9:16 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

rline wrote: So in terms of thinking about notation for this, since it's not face turning (which Konrad's notation lends itself to), is there an acceptable way to talk about turns, using the same kind of notation? Well we could label it like the faces of an icosahedron but I'd prefer to just label the vertices. We probably only need to label 10 vertices because all useful routines are only going to use half the puzzle or less anyways. My preference is still for Gelatinbrain's notation because his program is such a powerful tool to test and share routines. Also, I basically only ever think about routines in terms of their "form" rather than their notation. So, for example I think of the sequence as [[1:[1:1]],1] plus a few more details about how the pieces relate to each other. I'm always amazed when folks know and can recite notation for the Rubik's cube or any other puzzle so smoothly.
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rline

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Fri Dec 07, 2012 2:26 am 

Joined: Mon Feb 28, 2011 4:54 am

I'd like to share with you all my solving odyssey. It's only a spoiler if you class my approach as a spoiler. I think Burgo will be happy with this. I decided to try and approach it from the bottom up, rather than solving all piece types at once. I've surprised myself. The longest commutator used so far is a [3:1] and that was only on the last step. Everything else was done with simple turns and lots of thought, including [1:1] commutators. It took me a number of hours, mainly because of the turning of the puzzle. Here's what happened. 1. Solve down face, white in my case (forgot to take a photo but you can see it in the next few pics ) 2. Solve lower equator edges with their adjoining petals. (it's not floating, I had to rotate the pic) Attachment:
shot0000.JPG [ 80.05 KiB  Viewed 8320 times ]
3. Solve middle equator edges Attachment:
shot0001.png [ 344.14 KiB  Viewed 8320 times ]
4. Solve petals (and 2 triangles) below the middle equator edges. Attachment:
shot0002.png [ 369.96 KiB  Viewed 8320 times ]
5. Solve the little triangle above the down face edge. This was a quick step but I found it necessary to do this in order to be able to continue. Attachment:
shot0003.png [ 365.83 KiB  Viewed 8320 times ]
6. Solve remaining petal on each of the lower faces. Attachment:
shot0004.png [ 351.17 KiB  Viewed 8320 times ]
(Now looking at the puzzle with the top face as up) 7. Solve remaining edges Attachment:
shot0005.png [ 355.08 KiB  Viewed 8320 times ]
8. Solve lower petals on upper faces Attachment:
shot0006.png [ 368.53 KiB  Viewed 8320 times ]
9. Solve remaining petals Attachment:
shot0007.png [ 349.37 KiB  Viewed 8320 times ]
10. Solve centers Attachment:
shot0008.png [ 357.94 KiB  Viewed 8320 times ]
And now I'm stuck!
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Last edited by rline on Sat Dec 08, 2012 6:27 pm, edited 1 time in total.


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Konrad

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Fri Dec 07, 2012 5:57 am 

Joined: Thu Sep 17, 2009 6:07 am Location: Germany, Bavaria

Quite an achievement, rline! I had figured out already, that the little triangles are the tricky part. My shortest move sequence contains 30 moves Brandon's 12 move commutator is much shorter. I have not yet analysed, how he could isolate a triangle with so few turns. The other piece types are easy. When I wrote yesterday Konrad wrote: rline wrote: ...So Konrad, I take it by this that you're saying it will be quite a challenging solve? Will you be using commutators for most things? Yes to both questions (probably more tedious than really hard, but very easy to screw it up), but, please [my moderator self is watching me ], not more about solving in this thread. When the time comes, we can start a topic in the Solving Forum. , I was referring to the small triangles. Solving 60 of them with a sequence 30 moves long seemed to be tedious and error prone. I have not yet the time myself for a scramble and solve (I'll first lubricate and break in the puzzle). (I'm really curious how much time other puzzle addicts have left over for social life My promotion to a moderator didn't improve things much ) Regarding notation: It may be an overkill, but I have made a proposal for the notation of turns here. At least for me, names like L = Left are much easier to recollect than the mathematically correct Gelatinbrain scheme. I do not have a very good visual memory, so, I recollect things in a more abstract way. This is why I need a notation that can be easily remembered. I'm open to any suggestions for improvements! Naming specific pieces by turns which affect them produces pretty long "signatures". This is not any better with Gelatinbrain notation. Some tems I would use in a very visual sense:  "Face" as on a FTD; what we see as a face, not what we turn.  "Center" what looks like a center; corresponds to a corner of the FTI (2.1.1)  "Vertex" what we turn (corresponds to a face to be turned on the FTI 2.1.1)  "Edge" the 30 pieces with two stickers  "Petal" the large pieces on a face; obviously the reason why it got the name of the flower Bauhinia  "Triangles" the tricky triangles mentioned above If I ever post a move sequence here, I'll use both, the Gelatinbrain version and my own intuitive notation. I'm not sure if the "tricky triangles" can be solved by shorter sequences or if there is a reduction method as on the Crazy 3x3x3s. EDIT: Here is a proposal to use small letters for the faces of the Rex/Bauhinia. (Maybe we call it just RexB as a shortcut?) EDIT: Corrected a minor typo in the Gelatinbrain notation. Thanks Brandon for the hint
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martywolfman

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Fri Dec 07, 2012 6:43 am 

Joined: Tue Sep 11, 2012 1:51 pm Location: Bedford, England

haha. while i don't own one of these (yet...hopefully! ) That looks like a very...ummmm...interesting situation to try to solve, rline!
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Brandon Enright

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Fri Dec 07, 2012 6:44 am 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

I'm boarding a plane so I'll keep this short. 12 moves is the shortest pure commutator for the triangles. If there is a shorter sequence it would either not be pure (I have not looked for one) or not be of standard commutator form (I don't know of one).
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Konrad

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Fri Dec 07, 2012 6:55 am 

Joined: Thu Sep 17, 2009 6:07 am Location: Germany, Bavaria

martywolfman wrote: haha. while i don't own one of these (yet...hopefully! ) That looks like a very...ummmm...interesting situation to try to solve, rline! I'm afraid this a standard situation after the easy part
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Puzzlemad

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Fri Dec 07, 2012 6:56 am 

Joined: Mon Feb 27, 2012 10:57 am Location: In my study drooling over my puzzle hoard  Precioussssss!

I think postie tried to deliver mine yesterday and failed  so I will need to pick it up on saturday! Looking at this discussion, I have an awful sinking feeling that I will not be able to solve this without a tutorial. I'll give it a go but suspect that Rline's fantastic site will be giving me more clues again! I have tended to solve all my cubes by an adaptation of existing algorithms. I have never really understood how you all come up with commutators  I understand what they are but have no clue how to go about designing them. As for notation  I really like the one designed by Konrad  it is understandable by a human in front of a puzzle rather than a computer in front of a simulation of a puzzle. It is far nicer to be told to turn the UFR than ABC vertex. Thank you Konrad.
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Konrad

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Fri Dec 07, 2012 7:49 am 

Joined: Thu Sep 17, 2009 6:07 am Location: Germany, Bavaria

Puzzlemad wrote: ...I have tended to solve all my cubes by an adaptation of existing algorithms. I have never really understood how you all come up with commutators  I understand what they are but have no clue how to go about designing them..... Don't be afraid too much, Kevin. As I said, I have not scrambled and solved mine (My wife is looking at me suspiciously while I'm typing this. I'm expected to do other things. ), but this thread contains most likely enough hints already. What have I done so far? Actually, I used Gelatinbrain 2.1.1  the normal Face Turning Icosahedron  to find all necessary sequences. 2.1.1 contains the same pieces as the RexB but it has a different shape and 20 colours instead of 12. I did not bother with jumbling / unjumbling, so far. If you have problems running Gelatinbrain on your Mac, things become more difficult. Some may consider the usage of tools like Gelatinbrain as cheating, but then having solved hundreds of twisty puzzles before, could be considered as cheating as well. The requirement "Start with a fresh brain" is not easily fulfilled.
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unirox13

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Fri Dec 07, 2012 9:22 am 

Joined: Sun Aug 21, 2011 4:45 pm

Can someone post a few links to places that describe commutators and how to create them? I mostly understand what they are and can usually identify them when I see one written out. Aside from that I have very little knowledge of them. I'm hoping to get a few more complex puzzles over the next few weeks and I'd really like to stand a chance of solving them without a tutorial.
Thanks


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Konrad

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Fri Dec 07, 2012 10:43 am 

Joined: Thu Sep 17, 2009 6:07 am Location: Germany, Bavaria

I think a good introduction to commutators is here. And about conjugates conjugates as well. Brandon (=bmenrigh = Brandon Enright) has made a brilliant video introduction using Gelatinbrain here. EDIT: Let me add some explanation of Brandon's move sequence in the first post of this topic bmenrigh wrote: ...Up to this point the puzzle is very easy but the remaining 60 small triangles left are a bit trickier. There is a [5,1] or [3,3] commutator to cycle them. There is some variation to this so you can play with the structure of the commutator to find one that works nicely for you. Here is one example [KDG, EDK', EJF, EDK, KDG', DCG', KDG, EDK', EJF', EDK, KDG', DCG]... We write commutators as [X,Y]. This translates to sequence X followed by sequence Y, followed by the inverse sequence of X and finally the inverse of Y. To create a pure commutator the move sequence X has to isolate one piece. In this case the first five turns isolate a triangle. I'll use Gelatinbrain 1.2.3 to show how the (originally solved) puzzle looks after the first five turns. Now we turn the layer DCG with the isolated triangle counterclockwise by DCG'. The important thing to note is, that after doing the whole sequence of the first five moves backwards, the triangle that has replaced the isolated purple one by the sixth move will travel backwards to the original location from where the purple came (in this case in the purple face). We have constructed a commutator that does a pure 3cycle of triangles! As it happens, the first five moves are nested conjugates of the type [1:[1:1]]. The numbers in this type of notation show just the number of moves that have to be done. We write conjugates in a shortcut as [X:Y] which translates to X Y X'. If you have found a useful sequence Y, X is usually called a Setup Sequence. [[DGK:[KED':EJF]],DCG'] is the short notation for the 12 moves. This translates to my notation as [DR:[D':FDL]],FDR'] and the complete 12 move sequence in my notation is: DR D' FDL D DR' FDR' DR D' FDL' D DR' FDR. So, instead of remembering the whole sequence, you can memorize the pattern [[1:[1:1]],1] and the turns DR D' FDL FDR'. The result of Brandon's commutator is on 1.2.3 A generic commutator of this structure can be written as[[X1:[X2:X3], X4]. Because X1, X2, X3, X4 ar just single turns, the result is in this example a pretty short commutator. EDIT2: Here is the result of Brandon's commutator on a solved RexB. (Notation as above.) For this piece type Gelatinbrain 1.2.3 is a good choice. As Brandon has mentioned above, the corners of 1.2.3 do not exist on the RexB and vice versa the edges of the RexB do not exist on 1.2.3.
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rline

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Fri Dec 07, 2012 2:57 pm 

Joined: Mon Feb 28, 2011 4:54 am

Quote: Looking at this discussion, I have an awful sinking feeling that I will not be able to solve this without a tutorial. I'll give it a go but suspect that Rline's fantastic site will be giving me more clues again! I have tended to solve all my cubes by an adaptation of existing algorithms. I have never really understood how you all come up with commutators  I understand what they are but have no clue how to go about designing them. Kevin and unirox13, if I can do it, you can do it. And actually, I didn't use gelatinbrain at all. I opened it and had a look but because the exact puzzle isn't there, I decided to try and do it on the fly with a real puzzle. I wouldn't normally do that but this time I did. There's something intensely satisfying about being faced with a "stuck" situation and then thinking through a way to get around it. There were a few of them along the way. I also have not given up on doing the triangles without resorting to long or nonmemorable commutators. Konrad's post above is, as always, really helpful regarding commutators. (And I agree with him about the notation as well) But you (Kevin) already know exactly what a commutator is: the corner piece series is a great example of a [3,1] and the edge piece series is an example of a [1,1]. If you understand that in the CPS, the URU' is the 3 (which isolates the corner), then the L' is the 1 (which moves it out of place and puts another in its place), then the UR'U' is the undoing of the 3, then the L is the undoing of the 1, then you understand commutators. Any commutator on any other puzzle is exactly the same idea. And coming up with them is the same principle, it's just on a lot of puzzles they're harder to find. Which is why gelatinbrain and other simulators are used a fair bit to come up with them (to save accidentally scrambling the puzzle). To me, after having nearly solved the rex dodec once, I'd say that if there is a nice way to deal with the triangles then this puzzle will fall into the category of "just right". A good solve, challenging, interesting, but not impossible. At least with my approach above I've cut the triangles down to 30 instead of 60
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Konrad

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Fri Dec 07, 2012 4:30 pm 

Joined: Thu Sep 17, 2009 6:07 am Location: Germany, Bavaria

A bit of a warning: I have lubricated the puzzle and started to break it in. Two of the tiny triangles came off after a few turns. I think it is better to start with lubrication and breaking in and do the stickering afterwards (after a careful cleaning of the surface). Now, I'll use tiny drops of superglue to fix the little triangles.
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rline

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Fri Dec 07, 2012 5:03 pm 

Joined: Mon Feb 28, 2011 4:54 am

Konrad wrote: A bit of a warning: I have lubricated the puzzle and started to break it in. Two of the tiny triangles came off after a few turns. I think it is better to start with lubrication and breaking in and do the stickering afterwards (after a careful cleaning of the surface). Now, I'll use tiny drops of superglue to fix the little triangles. I want to comment along these lines also. I've spent quite a bit of time tensioning screws, lubricating, pulling the puzzle half apart, lubricating again, etc. I think there are similar issues to the points catching, but very minor. The little stickers would do well with some superglue. I can't see how they could do it any differently and still keep the puzzle at a manageable size. I also think the design is very good and I don't want that catching comment to take away from this puzzle. I've found that the screws needed to be loosened, but not very much. I suspect that after solving it quite a bit, it'll become better and better.
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Doug Roth

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Fri Dec 07, 2012 5:09 pm 

Joined: Sun May 29, 2011 2:56 pm Location: New York

Konrad wrote: A bit of a warning: I have lubricated the puzzle and started to break it in. Two of the tiny triangles came off after a few turns. I think it is better to start with lubrication and breaking in and do the stickering afterwards (after a careful cleaning of the surface). Now, I'll use tiny drops of superglue to fix the little triangles. Yes. This is what I always do, and it is much better than lubing after stickering. Another reason why you should lube first is that the lube can get on the stickers, and that can be really annoying. Doug
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Brandon Enright

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Fri Dec 07, 2012 5:47 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

I poked around some more and the shortest nonpure triangle 3cycle is [3,1]. Here is an example: [FAE', CDA, FAE, AFB', AEF', DAC', AEF, AFB]
Unfortunately that sequence cycles a petal piece along with each triangle so if you want to solve the petals last you'll need a pure 3cycle for them instead. The shortest one I can find is this [3,5] (equivalent to a [7,1]): [EDK', KDG, EDK, FAE, ADE, CDA', ADE', FAE', EDK', DGK', EDK, FAE, ADE, CDA, ADE', FAE']
I'd be somewhat surprised if there was a shorter pure commutator for the petals.
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rline

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Fri Dec 07, 2012 5:57 pm 

Joined: Mon Feb 28, 2011 4:54 am

bmenrigh wrote: I poked around some more and the shortest nonpure triangle 3cycle is [3,1]. Here is an example: [FAE', CDA, FAE, AFB', AEF', DAC', AEF, AFB]
Unfortunately that sequence cycles a petal piece along with each triangle so if you want to solve the petals last you'll need a pure 3cycle for them instead. The shortest one I can find is this [3,5] (equivalent to a [7,1]): [EDK', KDG, EDK, FAE, ADE, CDA', ADE', FAE', EDK', DGK', EDK, FAE, ADE, CDA, ADE', FAE']
I'd be somewhat surprised if there was a shorter pure commutator for the petals. Thought you were getting on a plane?!
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Brandon Enright

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Fri Dec 07, 2012 6:07 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

rline wrote: Thought you were getting on a plane?! I was, I did, I'm off 5hour flight. Gave me plenty of time to think about things to try when I got home. I'm pretty out of ideas. I think leaving the small triangles to last is the best strategy. Solving the first 30 using intuition is fantastic and should really cut down on the effort needed to solve them.
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rline

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Fri Dec 07, 2012 6:24 pm 

Joined: Mon Feb 28, 2011 4:54 am

bmenrigh wrote: rline wrote: Thought you were getting on a plane?! I was, I did, I'm off 5hour flight. Gave me plenty of time to think about things to try when I got home. I'm pretty out of ideas. I think leaving the small triangles to last is the best strategy. Solving the first 30 using intuition is fantastic and should really cut down on the effort needed to solve them. Yeah that's what I thought. Although even though we leave them till last, I still have hope we can somehow match them with centers and then cycle the centertriangletriangle pieces into place. I think that might be easier.
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Brandon Enright

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Fri Dec 07, 2012 6:38 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

rline wrote: Yeah that's what I thought. Although even though we leave them till last, I still have hope we can somehow match them with centers and then cycle the centertriangletriangle pieces into place. I think that might be easier. I've thought about this but it seems exceptionally hard. You could cycle them in pairs, breaking the centers while you're at it, with [DEA, JFE, DEA', CDA', ADE, JFE', DEA', CDA]. Solving all 60 with this double 3cycle would take a lot of tricks. Then to finish you could solve the centers pure using this [3,7]: [EJF, EAD, EJF', JIF, JKL', LGH', HCB', LGH, LJK, JIF', EJF, EAD', EJF', JIF, LJK', LGH', HCB, LGH, LJK, JIF'] There is probably a shorter routine but that's the first one I spotted.
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rline

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Fri Dec 07, 2012 6:52 pm 

Joined: Mon Feb 28, 2011 4:54 am

bmenrigh wrote: I've thought about this but it seems exceptionally hard. You could cycle them in pairs, breaking the centers while you're at it, with [DEA, JFE, DEA', CDA', ADE, JFE', DEA', CDA]. Solving all 60 with this double 3cycle would take a lot of tricks.
Then to finish you could solve the centers pure using this [3,7]: [EJF, EAD, EJF', JIF, JKL', LGH', HCB', LGH, LJK, JIF', EJF, EAD', EJF', JIF, LJK', LGH', HCB, LGH, LJK, JIF']
There is probably a shorter routine but that's the first one I spotted. Well what I was thinking is this. The last step in my pictures above was cycling the centers. But even though it's basically just URU'L'UR'U'L it's not pure. Each center takes two triangles with it, and it's fairly nice and syymetrical about how it does it. So I had the idea of doing a setup or two to position a triangle next to its center, then cycling it around to another spot and sort of storing it there. Once I make a trianglecentertriangle piece I don't touch it until they're all done. Then, once they're all done, 3 or so of the exact same cycle finishes the puzzle. I figured that this would mean cycling the triangles would effectively only be using a [3,1] commutator. Which means once we're down to the last 30 triangles (and centers) we're only using [3,1]. What do you think about that scenario? (In fact I think if you adopt Konrad's proposed notation above, then doing URU'L'UR'U'L is the exact cycle.)
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Brandon Enright

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Fri Dec 07, 2012 7:10 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

rline wrote: bmenrigh wrote: I've thought about this but it seems exceptionally hard. You could cycle them in pairs, breaking the centers while you're at it, with [DEA, JFE, DEA', CDA', ADE, JFE', DEA', CDA]. Solving all 60 with this double 3cycle would take a lot of tricks.
Then to finish you could solve the centers pure using this [3,7]: [EJF, EAD, EJF', JIF, JKL', LGH', HCB', LGH, LJK, JIF', EJF, EAD', EJF', JIF, LJK', LGH', HCB, LGH, LJK, JIF']
There is probably a shorter routine but that's the first one I spotted. Well what I was thinking is this. The last step in my pictures above was cycling the centers. But even though it's basically just URU'L'UR'U'L it's not pure. Each center takes two triangles with it, and it's fairly nice and syymetrical about how it does it. So I had the idea of doing a setup or two to position a triangle next to its center, then cycling it around to another spot and sort of storing it there. Once I make a trianglecentertriangle piece I don't touch it until they're all done. Then, once they're all done, 3 or so of the exact same cycle finishes the puzzle. I figured that this would mean cycling the triangles would effectively only be using a [3,1] commutator. Which means once we're down to the last 30 triangles (and centers) we're only using [3,1]. What do you think about that scenario? (In fact I think if you adopt Konrad's proposed notation above, then doing URU'L'UR'U'L is the exact cycle.) Your proposed URU'L'UR'U'L cycle is the same one that I suggested as [DEA, JFE, DEA', CDA', ADE, JFE', DEA', CDA] modulo some orientation and direction differences. The center + 2triangle group that it 3cycles could be used to solve a lot of the triangles but I'm envisioning the end becoming very, very inefficient. You have to form perfect groups in order to cycle the last 9 pieces into place all at once. One of the things that makes this very hard is that you can't really change the orientation of a group of pieces without breaking up the group. Each Center + 2triangle group has 5 possible orientations per face. The chances of you have all three groups for the last cycle all perfectly positioned to be solved in one cycle is very low and setting it up for that situation would be very hard. Instead I'd use this center + 2triangle 3cycle as a way to solve many more of the 30 remaining triangles. Once you're down to the last 1015 triangles then you could switch to the harder [5,1] commutator to solve them purely. If you do come up with a way to semiefficiently cycle the groups, never resorting to using the [5,1] commutator then I'd certainly like to see that .
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Puzzlemad

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Sat Dec 08, 2012 5:14 am 

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Konrad

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Sat Dec 08, 2012 8:29 am 

Joined: Thu Sep 17, 2009 6:07 am Location: Germany, Bavaria

Kevin, the most important question is: Does Gelatinbrain run on your Mac right now? If not, the sequences shown by Brandon are hard to understand. In this case Brandon could possibly help you with trouble shooting your computer problems. I had problems on Windows 7 for a while, fortunately Gelatinbrain is stable on my laptop now. If it runs, you can just cut and paste the sequences into Gelatinbrain 1.2.3 and see what happens. The piece types in question exist on it. Unfortunately there is no direct equivalent of the RexB in Gelatinbrain. The sequence described by rline, U R U' L' U R' U' L , is just the well known 8 move commutator [U R U', L'] = CPS on a 3x3x3 executed on a vertex turning Dodecahedron. The names of the turns follow my notation above. It's not higher math at all, just practical move sequences. Without Gelatinbrain, Gelatinbrain notation is a bit like cryptology U R U' L' U R' U' L can be done quite easily on a real RexB. The result would be a 3cycle of groups of three pieces = centre + two adjacent triangles. EDIT: Here is a picture showing the result of the sequence above performed on Gelatinbrain 1.2.3 1.2.3 Centres = RexB centres 1.2.3 star points = RexB triangles
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Brandon Enright

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Sat Dec 08, 2012 10:41 am 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

Puzzlemad wrote: I did understand the very basics of the very simple commutator ideas from Konrad and Rline much higher up the thread but suddenly you've entered the stratosphere and I have no idea what you are talking about! I guess the long strings of letters don't help! Sorry You're right the long strings of letters are totally useless for a human to try to read. They're only useful for copyandpaste into Gelatinbrain's program or my tool for decomposing their structure. So for example, when you see me write "[EJF, EAD, EJF', JIF, JKL', LGH', HCB', LGH, LJK, JIF', EJF, EAD', EJF', JIF, LJK', LGH', HCB, LGH, LJK, JIF']" you can think of it as a serial number that describes some move in a catalog. If you have Gelatinbrain's program working then you can look it up and if you don't then ignore it. Here is what Gelatinbrain's program will show you: Attachment:
gb_1.2.3_center_3cycle.png [ 22.9 KiB  Viewed 7860 times ]
Since move sequences are so unwieldy I made this tool which can be used to tell you more about the routine. If you paste it in, the useful part is this: Sequence disassembled: [[EJF:EAD],[JIF:[JKL':[LGH':HCB']]]] Sequence form (shorthand): [[1:1],[1:[1:[1:1]]]] That tells you the structure of the routine and how the turns relate to oneanother. It still doesn't give you any physical meaning.
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gelatinbrain

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Sat Dec 08, 2012 3:00 pm 

Joined: Thu May 31, 2007 7:13 pm Location: Bruxelles, Belgium

Konrad wrote: Unfortunately there is no direct equivalent of the RexB in Gelatinbrain.
It is 1.2.1, although the shape is different. As for my notation, I admit it is not intuitive. But the basic rule is quite simple. 'A' for the central face, and clockwise from the top, 'B' to 'G' The sum of two opposite letters are all equal. 'A' + 'L' == 'B' + 'K' == , and so on. You don't even have to know the English. Memorizing the alphabetical order is enough
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Brandon Enright

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Sat Dec 08, 2012 7:13 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

I updated my Gelatinbrain Sequence Utility to support outputting Kondrad's VTD notation. Now if you enter "[EJF, EAD, EJF', JIF, JKL', LGH', HCB', LGH, LJK, JIF', EJF, EAD', EJF', JIF, LJK', LGH', HCB, LGH, LJK, JIF']" and choose Konrad's VTD notation for output you'll see "[FDL, F, FDL', L, DBL', BR', UR', BR, DBL, L', FDL, F', FDL', L, DBL', BR', UR, BR, DBL, L']". I still wouldn't want to try to do a 20move sequence on a physical puzzle by following notation. Seems very errorprone to me.
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Konrad

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Sun Dec 09, 2012 4:22 am 

Joined: Thu Sep 17, 2009 6:07 am Location: Germany, Bavaria

gelatinbrain wrote: Konrad wrote: Unfortunately there is no direct equivalent of the RexB in Gelatinbrain.
It is 1.2.1, although the shape is different... Hey Gelatinbrain, did you mean 2.1.1? (1.2.1 is just the Dino Dodecahedron) It was mentioned above that 2.1.1 corresponds to the RexB. Still, personally I have used 2.1.1 finding the necessary commutators. (Just for the triangles of the RexB my own sequence is 30 moves long and I'll use Brandon's for a physical solve. I have yet to fix the triangular stickers with super glue.) Unfortunately, the colour scheme and shape is different. (2.1.1 is harder, because you have to care about orientations and more colours of stickers on one piece than on the RexB. That's why Brandon had asked for different sticker sets ) I admire your work and your program tremendously, and if the effort is not too high, could you add the RexB as a directly correspondent VTD? In any case, thank you very much for your great contributions!!! BTW, I have a technical problem with chosing VTD puzzles beyond number 1.2.46. I see that there is something below, but cannot see what. (Gelatinbrain version 1.20710, Windows 7, screen resolution 1366x768) I wanted to check, if you have possibly added a better fitting (closer to RexB) puzzle, lately.
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rline

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Sun Dec 09, 2012 4:26 am 

Joined: Mon Feb 28, 2011 4:54 am


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gelatinbrain

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Sun Dec 09, 2012 6:37 am 

Joined: Thu May 31, 2007 7:13 pm Location: Bruxelles, Belgium

Konrad wrote: Hey Gelatinbrain, did you mean 2.1.1? (1.2.1 is just the Dino Dodecahedron) It was mentioned above that 2.1.1 corresponds to the RexB. Sorry, I mistyped. It's 1.2.11. Although the shape is different, and although I agree that that curved cuts are more elegant, I think fuctionnay they are equivalent. Konrad wrote: BTW, I have a technical problem with chosing VTD puzzles beyond number 1.2.46. I see that there is something below, but cannot see what. Your monitor is too small or the menu is too big. But don't worry you can click and select them anyway. Later I will divide the menu into two
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Doug Roth

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Sun Dec 09, 2012 9:33 am 

Joined: Sun May 29, 2011 2:56 pm Location: New York

gelatinbrain wrote: Konrad wrote: Hey Gelatinbrain, did you mean 2.1.1? (1.2.1 is just the Dino Dodecahedron) It was mentioned above that 2.1.1 corresponds to the RexB. Sorry, I mistyped. It's 1.2.11. Although the shape is different, and although I agree that that curved cuts are more elegant, I think fuctionnay they are equivalent. Konrad wrote: BTW, I have a technical problem with chosing VTD puzzles beyond number 1.2.46. I see that there is something below, but cannot see what. Your monitor is too small or the menu is too big. But don't worry you can click and select them anyway. Later I will divide the menu into two Yes, it seems that that is equivalent to the RexB, and all of the commutators already listed in this thread work correctly on 1.2.11. Doug EDIT: After checking the scores on GB, there have already been a few virtual solves by boublez, schuma, Agamemnon, Sjoerd, Brandon, Julian, and Alaskajoe.
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Konrad

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Sun Dec 09, 2012 2:30 pm 

Joined: Thu Sep 17, 2009 6:07 am Location: Germany, Bavaria

bmenrigh wrote: I updated my Gelatinbrain Sequence Utility to support outputting Kondrad's VTD notation. ... I still wouldn't want to try to do a 20move sequence on a physical puzzle by following notation. Seems very errorprone to me. Thank you Brandon for adding the translation to my VTD notation. I do not understand the second sequence above. This remark has nothing to do with my notation, right?. If you are ever going to use the sequence, you have to memorize it somehow. Instead of memorizing [[EJF:EAD],[JIF:[JKL':[LGH':HCB']]]] (shorthand): [[1:1],[1:[1:[1:1]]]] it would become in my notation [[FDL:F], [L:[DBL':[BR':UR']]]] This is still a tough thing to memorize, but independent on notation, right? Did you want to express that it is easier to memorize this in a visual way? Or do you want to say that a method should avoid such a long sequence at all? (Which would eliminate a method that does centres last.)
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Brandon Enright

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Sun Dec 09, 2012 2:36 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

No it has nothing to do with your notation The point I was trying to make is that memorizing a 20move routine is quite hard so you'd probably need to write the notation down and then try to follow the notation each time you do the sequence. Even following notation seems like it would be hard and errors would be likely. What I should have said is that I don't think you should save centers until last because the shortest routine I can find for them is 20 moves.
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schuma

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Sun Dec 09, 2012 3:39 pm 

Joined: Thu Jul 23, 2009 5:06 pm Location: Berkeley, CA, USA

Doug Roth wrote: EDIT: After checking the scores on GB, there have already been a few virtual solves by boublez, schuma, Agamemnon, Sjoerd, Brandon, Julian, and Alaskajoe. Another way to play this puzzle on computer (windows only): Download Magic Tile v2 from: http://www.gravitation3d.com/magictile/And select Puzzle > Elliptical > Sphere > Dodecahedron > Vertex Twisting > V2:0:0 It's just another view of the same puzzle. By the way, on my computer I need to turn setting > debug > Enable Texture Mipmaps to False, otherwise the animation is just very slow. This program also supports macro. According to MagicTile v2's scoreboard, Eduard Baumann solved it.
Attachments: 
Image 000.png [ 32.48 KiB  Viewed 7600 times ]



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Konrad

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Sun Dec 09, 2012 3:58 pm 

Joined: Thu Sep 17, 2009 6:07 am Location: Germany, Bavaria

bmenrigh wrote: ...What I should have said is that I don't think you should save centers until last because the shortest routine I can find for them is 20 moves. Aah, OK. I agree with this
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rline

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Sun Dec 09, 2012 7:46 pm 

Joined: Mon Feb 28, 2011 4:54 am


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Brandon Enright

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Sun Dec 09, 2012 8:18 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

rline wrote: Here's one for the notation buffs...
I found a triangle 3cycle which moves the pieces shown below in the pic.
According to Konrad's notation, it cycles pieces from the l (left) face to the ul (upleft) face across to the r (right) face. But I have no idea how to correctly identify the pieces. Any ideas? I don't think there is a generally decided "correct" way to notate these pieces. My preference would be for listing the "grips" (vertices) that move a given piece. Each triangle is moved by four different vertices so to list them would make the position of the triangle on the L face the {UL, L, FDL, FL} position. The triangle on the UL face is in the {U, BL, L, UL} position and the triangle on the R face is in the {UR, R, FDR, FR} position.
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rline

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Sun Dec 09, 2012 9:00 pm 

Joined: Mon Feb 28, 2011 4:54 am

bmenrigh wrote: rline wrote: Here's one for the notation buffs...
I found a triangle 3cycle which moves the pieces shown below in the pic.
According to Konrad's notation, it cycles pieces from the l (left) face to the ul (upleft) face across to the r (right) face. But I have no idea how to correctly identify the pieces. Any ideas? I don't think there is a generally decided "correct" way to notate these pieces. My preference would be for listing the "grips" (vertices) that move a given piece. Each triangle is moved by four different vertices so to list them would make the position of the triangle on the L face the {UL, L, FDL, FL} position. The triangle on the UL face is in the {U, BL, L, UL} position and the triangle on the R face is in the {UR, R, FDR, FR} position. Wow, that's horrible! Not your explanation, just the way we might have to notate. I think I'd rather not notate at all! I wonder whether it would work referring to the edge which the triangle points to, given that it points away from the center pentagon? And we state the face it's on first. So my triangle on the right face would be the RBR triangle. I guess I could say I cycled R/BR > L/BL > BL/L. Or even using r(br) > l(bl) > bl(l).
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Brandon Enright

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Sun Dec 09, 2012 9:28 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

rline wrote: Wow, that's horrible! Not your explanation, just the way we might have to notate. I think I'd rather not notate at all!
I wonder whether it would work referring to the edge which the triangle points to, given that it points away from the center pentagon? And we state the face it's on first. So my triangle on the right face would be the RBR triangle. I guess I could say I cycled R/BR > L/BL > BL/L.
Or even using r(br) > l(bl) > bl(l). Yeah it is pretty cumbersome. Your suggestion would work but it's specific to this puzzle and requires that you first define what a "triangle" so that it isn't confused with an edge or some other piece. This is probably not an issue in the real world but it does lack some mathematical elegance. Your notation method also depends a bit on the external geometry of the puzzle. The triangles on an FTI look like "edgewings" and you'd have to create another notation for them. My suggestion still uniquely and unambiguously describes these pieces no mater what the shape of the puzzle is.
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rline

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Sun Dec 09, 2012 11:05 pm 

Joined: Mon Feb 28, 2011 4:54 am

Well, I have finally solved my rex dodecahedron. I'd gotten to only triangles remaining a few times before, but today I decided to actually solve the whole thing. I am particularly pleased with this cause 1) I spent a long time on those pesky triangles at the end (and I only had around half of the triangles to do instead of the full 60), and 2) this was despite some indifferent turning and a number of pops during the solve, at least one of which involved a couple of pieces that I may or may not have put back in correctly. It's made me more convinced that solvng all the triangles at the end is a recipe for insanity. Even with my [4,3] commutator, the trickiest part was some of the setup moves required to put the triangles into position. Ridiculous! I actually had to think hard about it. Welll, at least I know my method works. It's a really fun and thoughtful method up until the end, where you just want to "get the stupid triangles done".
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Konrad

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Mon Dec 10, 2012 1:08 pm 

Joined: Thu Sep 17, 2009 6:07 am Location: Germany, Bavaria

bmenrigh wrote: I'm boarding a plane so I'll keep this short. 12 moves is the shortest pure commutator for the triangles. If there is a shorter sequence it would either not be pure (I have not looked for one) or not be of standard commutator form (I don't know of one). rline wrote: .... Even with my [4,3] commutator, the trickiest part was some of the setup moves required to put the triangles into position. ... Hi rline, your 14 move sequence is a 4cycle, right? Setups for 4cycles are much harder than for 3cycles, I think. Have you ever looked at Brandon's [5,1] (or more detailed [[1:[1:1]], 1]): [[KDG:[EDK':EJF]],DCG'] = KDG, EDK', EJF, EDK, KDG', DCG', KDG, EDK', EJF', EDK, KDG', DCG = DR, D', FDL, D, DR', FDR', DR, D', FDL', D, DR', FDR (translated to Konrad's VTD notation) You can look at one of my posts above. I find Brandon's sequence easy to memorize and shortest should be short enough. Would you like to share your [4,3]? Regarding notation for pieces: I guess, the best way to avoid a cumbersome notation is a picture / diagram like in Gelatinbrain. BTW, I have fixed the triangular stickers with superglue. Before I go on solving the RexB, I'll just turn it for some hours breaking it in. I find it more annoying, if a puzzle catches while solving it. I prefer breaking it in in a casual way, e.g. while watching TV. I will not change the tension for the time being. My silicone spray improved the turning a lot. Sometimes, a looser puzzle starts catching more.
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Brandon Enright

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Mon Dec 10, 2012 1:25 pm 

Joined: Thu Dec 31, 2009 8:54 pm Location: Bay Area, California

Hi Konrad, a 4cycle isn't possible (odd permutation). A 5cycle would be possible.
I reverseengineered rline's [4,3] sequence from his picture. It is GB: [ACD', AEF, ACD, AEF', ABC, DCG, ABC', AEF, ACD', AEF', ACD, ABC, DCG', ABC'] KVTD: [FR', FL, FR, FL', UFR, FDR, UFR', FL, FR', FL', FR, UFR, FDR', UFR']
It's actually trivial to truncate it to a [3,3]: GB: [ACD', AEF, ACD, ABC, DCG, ABC', ACD', AEF', ACD, ABC, DCG', ABC'] KVTD: [FR', FL, FR, UFR, FDR, UFR', FR', FL', FR, UFR, FDR', UFR']
Notice that the X Y X' Y' in rline's construction works not because it is a commutator but because the first three moves are a conjugate. The last AEF' / FL' move has nothing to do with the ABC, DCG, ABC' / UFR, FDR, UFR' portion and can be left off.
EDIT: Also note that a [4,3] can always be converted to a [6,1] and a [3,3] can always be converted to a [5,1]. I actually found my [5,1] as a [3,3] (because it's easier to find that way for me) and then converted it later.
EDIT 2: BTW rline's sequence is equivalent to a rotation of mine:
Mine: [KDG, EDK', EJF, EDK, KDG', DCG', KDG, EDK', EJF', EDK, KDG', DCG]
Rotate sequence left 2 moves (an inverse reorientation of rline's): [EJF, EDK, KDG', DCG', KDG, EDK', EJF', EDK, KDG', DCG, KDG, EDK']
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Konrad

Post subject: Re: How to solve the Rex / Bauhinia Dodecahedron Posted: Mon Dec 10, 2012 1:47 pm 

Joined: Thu Sep 17, 2009 6:07 am Location: Germany, Bavaria

bmenrigh wrote: Hi Konrad, a 4cycle isn't possible (odd permutation). A 5cycle would be possible. I was mislead by this remark rline wrote: ...I found a pure triangle sequence which is 14 moves long. It's a [4,3] commutator. Only issue is that it cycles triangles across 4 faces, which is not ideal when really 3 is the most I want. Hopefully I can alter it. @rline, what did you mean by "across four faces"? bmenrigh wrote: I reverseengineered rline's [4,3] sequence from his picture. It is GB: [ACD', AEF, ACD, AEF', ABC, DCG, ABC', AEF, ACD', AEF', ACD, ABC, DCG', ABC'] KVTD: [FR', FL, FR, FL', UFR, FDR, UFR', FL, FR', FL', FR, UFR, FDR', UFR'] How on earth can you do this reverseengineering? You are just looking at rline's picture and you can tell what he did? Wow!
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