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perfredlund

Post subject: Re: Patterns Posted: Mon Apr 30, 2012 6:47 am 

Joined: Fri May 06, 2005 10:13 am Location: Norway

A new contribution towards our Ring variations completion: 6 Rings (r,u,l,b,d,f) (29 m).It is the inverse of the listed missing 6 Rings (r,f,d,b,l,u). Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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perfredlund

Post subject: Re: Patterns Posted: Thu May 03, 2012 7:11 am 

Joined: Fri May 06, 2005 10:13 am Location: Norway

Another Rings patterns contribution. 6 Rings (f,b,u,d,r.l) (29m).It is simply composed of 2 already posted ring patterns. 2 turns cancelled out Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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perfredlund

Post subject: Re: Patterns Posted: Fri May 04, 2012 4:28 am 

Joined: Fri May 06, 2005 10:13 am Location: Norway

I improved an already posted 4 Rings pattern. 4 Rings (u,f,d,r) (33 m).Again combining 2 ring patterns and cancelling 2 turns. Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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glazik

Post subject: Re: Patterns Posted: Fri May 04, 2012 11:04 am 

Joined: Wed Oct 12, 2011 12:54 pm

@ Per Algorithms similar to your 3 last ones were already published on Walter's website (same length  transformed by inversion/symmetry). The group of rings algorithms was already complete, so it would be best to concentrate on improving the published algorithms. The 2 longest algorithms that could certainly be improved are those of: (u,r,b,l,d) (36 moves) (r,f,b,l,d,u) (39 moves) Unfortunately, I haven't found any shorter solutions for these two, up to now Here is a list of a few slightly improved algorithms (1 move less only): 5 Rings (r,f)(d,l,b) (23 moves)WR WF' WR' VF WR' F2 WR NF' NB' WR' F2 WR NF WR' F WR MF' WR' F' WR MR MF MR' 5 Rings (r,f)(d,l,b) (23 moves)6 Rings (r,l)(b,f,u,d) (24 moves)WU' WR2 WU WF' MU F MU WF2 MU' F' MU' WF' NR2 U2 B2 NL SF2 NR' F2 U2 NL2 MU' MR2 MU 6 Rings (r,l)(b,f,u,d) (24 moves)6 Rings (r,f,u,l,b,d) (12 moves)WR WF' WR VF2 NL2 MF2 VR2 NF' NB' MR MF MR' 6 Rings (r,f,u,l,b,d) (12 moves)6 Rings (r,f,u,d,l,b) (23 moves)WR WF' WR' VF WU F2 WU' NF' NB' WU F2 WU' NF WU F WU' MF' WU F' WU' MR MF MR' 6 Rings (r,f,u,d,l,b) (23 moves)6 Rings (r,d,u,b,f,l) (28 moves)VB' R2 NB NF R2 NB' WU' NF' R2 NB NF R2 NB' MR D MR' WU' MR D' MR' WF' VL2 NU2 MF MR2 MF' VD2 NL2 6 Rings (r,d,u,b,f,l) (28 moves)


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perfredlund

Post subject: Re: Patterns Posted: Sun May 06, 2012 5:29 am 

Joined: Fri May 06, 2005 10:13 am Location: Norway

Hmmm. I cannot find the professor Ring patterns on that webpage. Give me a link please Kind regards, Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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glazik

Post subject: Re: Patterns Posted: Sun May 06, 2012 8:31 am 

Joined: Wed Oct 12, 2011 12:54 pm

Hi Per, Click the link below for displaying the 3 Rings (u,r,f) page: Ring Patterns  5x5x5 CubeOther patterns can be selected in the lefthandside window.


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perfredlund

Post subject: Re: Patterns Posted: Mon May 07, 2012 5:33 am 

Joined: Fri May 06, 2005 10:13 am Location: Norway

Hi! I found an improvement to an existing case. 5 Rings (r,d,f,u,l) (33 m).It is equivalent to 5 Rings (u,r,b,l,d) by symmetry. So quite a nice improvement  by just combining 2 known ring patterns ... Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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perfredlund

Post subject: Re: Patterns Posted: Wed May 09, 2012 7:12 am 

Joined: Fri May 06, 2005 10:13 am Location: Norway

I guess this is my last Rings contribution for a while ... I improved an existing case. Equivalent to (r,f,b,l,d,u) ... 6 Rings (f,b,u,r,l,d) (35 m).Yet again combining 2 other ring patterns. Quite a lot of transformation work though ... Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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Waran

Post subject: Re: Patterns Posted: Tue May 15, 2012 4:57 pm 

Joined: Sat Jan 28, 2006 6:04 am Location: Switzerland

I just found an alternative solution for the 'Gridlock' pattern which saves 5 moves: GridlockMR' U' MR MF D' MF' MR' U MR MF D MF2 R' MF MU L' MU' MF' R MF MU L MU2 F' MU MR B' MR' MU' F MU MR B MR' (34 btm) While we're on the 4x4x4, here are two more patterns for this cube: Winding HexagonR MD' L' U' L MD MU L' U L MU' R' L' MD' R D R' MD MU R D' R' MU' L TF MU' L2 MU MR MU' SR2 MU ML MU' R2 MU MR' ML' TF' (39 btm) 4 Woven RingsSD R' L' U2 F' B' U' F2 WR2 F2 MD TD TL TR TU2 TB TF SD2 MD TR' U MR D MR' U' WR D' R D ML D' TL' U ML D ML' U' WR' D' L D MR TD' (43 btm)


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Waran

Post subject: Re: Patterns Posted: Wed May 16, 2012 11:53 am 

Joined: Sat Jan 28, 2006 6:04 am Location: Switzerland

I slightly improved the '4 Woven Rings': 4 Woven RingsWF' WR WF WR' F' B' L2 (U D ML2 SD MR2 MF2 MR2 D2) L2 B F TR D2 F' U SF MD2 SF' U' SF MD2 B SD2 B' D SB MU2 SF D' SF' MU2 F U2 TR' (41 btm)


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Waran

Post subject: Re: Patterns Posted: Thu May 17, 2012 7:20 am 

Joined: Sat Jan 28, 2006 6:04 am Location: Switzerland

With some additional moves a scalable algorithm can be created: 4 Woven Rings (scalable version)SD R' L' U2 F' B' U' F2 SR2 B2 NU TB2 TR2 TL2 TF2 TU TB TF TU2 TR TL TU' TD SD2 ND TR' U NR D NR' U' NL' NR D' R D NL D' TL' U NL D NL' U' NL NR' D' L D NR TD' (51 btm) When you display the pattern just click on any of these links below the applet: Revenge Cube Â· Professor Cube Â· VCube 6 Â· VCube 7. The pattern is adapting itself to the corresponding cube size.


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glazik

Post subject: Re: Patterns Posted: Fri May 18, 2012 4:24 am 

Joined: Wed Oct 12, 2011 12:54 pm

Here is a slightly shorter version of the 4 Woven Rings (4x4x4 Cube). Unfortunately, it is not scalable WF' WR WF WR' F2 D2 R2 WU WF' MR2 WF WU' TR2 D2 F2 TF L2 U' R SU ML2 SU' R' SU ML2 D SL2 D' L SD MR2 SU L' SU' MR2 U R2 TF' 4 Woven Rings (38 moves)


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perfredlund

Post subject: Re: Patterns Posted: Tue May 22, 2012 8:38 am 

Joined: Fri May 06, 2005 10:13 am Location: Norway

I improved the Winding Hexagon (34 m) pattern. Breakdown: 1. TR (setup) 2. [NU F2 NU, TB] 3. [U F2 U, NB] 4. [NU B2 NU, TF] 5. [U B2 U, NF] 6. TR (undo setup) Basically only 4 8move commutators with setup Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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perfredlund

Post subject: Re: Patterns Posted: Wed May 23, 2012 12:14 pm 

Joined: Fri May 06, 2005 10:13 am Location: Norway

The Winding Hexagon pattern is scalable like so: Winding Hexagon (V6, 34m).This one is scaled unequally. It is also possible to scale equally. I will post that quite shortly Unfortunately it is impossible to scale to 5x5x5 (core restriction...) Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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Waran

Post subject: Re: Patterns Posted: Thu May 24, 2012 3:36 pm 

Joined: Sat Jan 28, 2006 6:04 am Location: Switzerland

Great algorithm improvements for the '4 Woven Rings' and the 'Winding Hexagon'! Finding algorithms which can display the same pattern on a range of other cube models is quite amazing. Often patterns look distorted when applied on other cubes so that new solutions have to be found. I was looking for 'Winding Hexagon' variations with different color arrangements. Here is a (not scalable) version with 4 colors per face: Winding Hexagon (with 4 colors per face):D' (U F' D SF MD2 SF' D' F SD B' MD2) (F R' B SR MB2 SR' B' R SF' L' MB2) (R U' L SD' ML2 SD L' U SR' D' ML2) D R2 D2 MU ML R MU' ML MU R' MU' MF' ML' MF ML' D2 R2 (51 btm or 50 btm actually)


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perfredlund

Post subject: Re: Patterns Posted: Thu May 31, 2012 7:45 am 

Joined: Fri May 06, 2005 10:13 am Location: Norway

Hi! I improved the Winding Hexagon (4 Colours per face) (43 m).First i permute 4 "chicken feet" like so: TD2 TF TR2 TD TR2 R L D2 R L U R L D2 R L U TR2 TD TR2 TF TD2 (5 first turns are setup). Then the last 2 "chicken feet" like so: F2 WD NB2 WD F WD NB2 WD NU2 R L U R L NU2 R L U R L F Quite a nice improvement The setup moves for first part allows other patterns to be deduced Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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perfredlund

Post subject: Re: Patterns Posted: Thu May 31, 2012 1:12 pm 

Joined: Fri May 06, 2005 10:13 am Location: Norway

Another pattern based on the setup moves TD2 TF TR2 TD TR2: Squared Hexagon (21 m).Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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perfredlund

Post subject: Re: Patterns Posted: Thu May 31, 2012 1:26 pm 

Joined: Fri May 06, 2005 10:13 am Location: Norway

Another surprise find with the same setup turns: Sorta CubeinCube (22 m).(Doable in 18 turns with 3cycles ) Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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perfredlund

Post subject: Re: Patterns Posted: Fri Jun 01, 2012 3:10 pm 

Joined: Fri May 06, 2005 10:13 am Location: Norway

It is possible to "scale" the Winding Hexagon (4 colour version, V6) (53 m).The last 10 turns are center correction turns Actually the 4x4x4 original version is a degenerate version Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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Waran

Post subject: Re: Patterns Posted: Sun Jun 10, 2012 11:47 am 

Joined: Sat Jan 28, 2006 6:04 am Location: Switzerland

@ Per Hey, you found very cool and short solutions! I am still fascinated by the hexagon that runs through all six faces of the cube. So the form of the hexagon is exactly the same but the colorization is different: Double Hexagon 1R MU L' U' L MU' MD' L' U L MD R' L' MU R D R' MU' MD' R D' R' MD L TF MU' L2 MU MR MU' SR2 MU ML MU' R2 MU MR' ML' TF' (39 btm) Double Hexagon 2MR' B' D B MR B' MR' D' MR B MD2 R' F U2 F' R MD2 R' F2 U' MF U F' U' MF' U' F' R TB2 SR' B R SF L' MB2 L SF' R' B' SR B2 MU2 R' MU MR MU' R MU MR' MU' F MU' MF' MB' MU F' MU' MB MF MU' (60 btm)


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glazik

Post subject: Re: Patterns Posted: Mon Jun 18, 2012 2:55 pm 

Joined: Wed Oct 12, 2011 12:54 pm

@ Walter The algorithms have been very slightly improved: Double Hexagon 1Edges L' MU R D R' MU' MD' R D' R' MD L L MB R' B' R MB' MF' R' B R MF L' Centers TL MD' F2 MD MB MD' SB2 MD MF MD' B2 MD MB' MF' TL' Double Hexagon 1 (37 btm)Double Hexagon 2Centers MU MF' MB' MU F MU' MB MF MU F' MU MR MU' R' MU MR' MU' R MU2 Edges MU TB2 SD' B' U' SB D MB2 D' SB' U B SD B' L' B' MU' B MU L MU' B' ML2 U F' R2 F U' ML2 U F2 R MF' R' F R MF R F U' Double Hexagon 2 (58 btm)


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schuma

Post subject: Re: Patterns Posted: Thu Jun 21, 2012 2:49 am 

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


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perfredlund

Post subject: Re: Patterns Posted: Fri Jun 22, 2012 3:07 pm 

Joined: Fri May 06, 2005 10:13 am Location: Norway

I improved the following pattern, by a new approach: Double Hexagon 1 (29 btm).The breakdown is like so: 1. D U R2 B WU2 R WU2 R B R2 D U (cycle dedges) 2. TU NB TR F2 TR NB TR F2 TR TU (bar 3cycle) 3. TU TF NR B2 NR TF NR B2 NR TU (bar 3cycle) 3 turns cancel out for good measure Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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perfredlund

Post subject: Re: Patterns Posted: Fri Jun 22, 2012 3:37 pm 

Joined: Fri May 06, 2005 10:13 am Location: Norway

glazik wrote: @ Walter The algorithms have been very slightly improved: Double Hexagon 1Edges L' MU R D R' MU' MD' R D' R' MD L L MB R' B' R MB' MF' R' B R MF L' Centers TL MD' F2 MD MB MD' SB2 MD MF MD' B2 MD MB' MF' TL' Double Hexagon 1 (37 btm)Double Hexagon 2Centers MU MF' MB' MU F MU' MB MF MU F' MU MR MU' R' MU MR' MU' R MU2 Edges MU TB2 SD' B' U' SB D MB2 D' SB' U B SD B' L' B' MU' B MU L MU' B' ML2 U F' R2 F U' ML2 U F2 R MF' R' F R MF R F U' Double Hexagon 2 (58 btm)The centres on the green face for version 2 are incorrect ... minor mistake i guess Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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Andrea

Post subject: Re: Patterns Posted: Fri Jun 22, 2012 3:43 pm 

Joined: Wed Apr 13, 2011 8:37 am Location: Germany

The Impossible Big EdgeAttachment:
superedge1.jpg [ 118.52 KiB  Viewed 7083 times ]
Attachment:
superedge2.jpg [ 115.51 KiB  Viewed 7083 times ]
Attachment:
superedge3.jpg [ 118.01 KiB  Viewed 7083 times ]
Exchange 2 corners and flip one edge. Both impossible on Rubik's Cube. These are 2 speceial parity cases on Mixup Plus.


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Waran

Post subject: Re: Patterns Posted: Sun Jun 24, 2012 9:26 am 

Joined: Sat Jan 28, 2006 6:04 am Location: Switzerland

glazik wrote: @ Walter The algorithms have been very slightly improved: Double Hexagon 1Edges L' MU R D R' MU' MD' R D' R' MD L L MB R' B' R MB' MF' R' B R MF L' Centers TL MD' F2 MD MB MD' SB2 MD MF MD' B2 MD MB' MF' TL' Double Hexagon 1 (37 btm)Double Hexagon 2Centers MU MF' MB' MU F MU' MB MF MU F' MU MR MU' R' MU MR' MU' R MU2 Edges MU TB2 SD' B' U' SB D MB2 D' SB' U B SD B' L' B' MU' B MU L MU' B' ML2 U F' R2 F U' ML2 U F2 R MF' R' F R MF R F U' Double Hexagon 2 (58 btm)perfredlund wrote: The centres on the green face for version 2 are incorrect ... minor mistake i guess I added setup moves to fix the center piece in the back face. Well, the pattern is actually a very nice color variation of the Winding Hexagon: Winding Hexagon 2B (MU MF' MB' MU F MU' MB MF MU F' MU MR MU' R' MU MR' MU' R MU2) B' MU TB2 SD' B' U' SB D MB2 D' SB' U B SD B' L' B' MU' B MU L MU' B' ML2 U F' R2 F U' ML2 U F2 R MF' R' F R MF R F U' (61 btm) perfredlund wrote: I improved the following pattern, by a new approach: Double Hexagon 1 (29 btm).Very clever approach! This way the centers doesn't have to be done seperately which saves a lot of moves.


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Waran

Post subject: Re: Patterns Posted: Sun Jun 24, 2012 9:49 am 

Joined: Sat Jan 28, 2006 6:04 am Location: Switzerland

@ Andrea Your pattern is indeed impossible to achive on a Rubik's Cube. So, here is a solution for a 4x4x4 cube which requires 15 moves: Impossible Big EdgeTD R2 TU' R2 TD' B2 TU B2 TD' B2 TU B2 TD' T3L2 WF2 (15 btm) I assume, your algorithm for the 'Mixup Plus Cube' must be completely different. @ schuma Your Dodecahedron pattern looks very nice, even without stickers. Do you have an algorithm for this?


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Andrea

Post subject: Re: Patterns Posted: Sun Jun 24, 2012 4:10 pm 

Joined: Wed Apr 13, 2011 8:37 am Location: Germany

Hi Waran, Quote: I assume, your algorithm for the 'Mixup Plus Cube' must be completely different.
Yes. After the parity, you must resolve the extended centers. The Mixup Cube works very different to the 4x4x4.


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glazik

Post subject: Re: Patterns Posted: Tue Jun 26, 2012 3:20 pm 

Joined: Wed Oct 12, 2011 12:54 pm

@ Per Double Hexagon 1A very tiny gain of 1 move can been obtained from this insertion: Insertion of TU TF MR' B2 MR TF' MR' B2 MR TU' into TU MB TR' F2 TR MB' TR' F2 TR TU': (TU) (MB TR' F2 TR MB') (TF MR' B2 MR TF' MR' B2 MR) (TR' F2 TR) (TU') Double Hexagon 1 (28 btm)@ Walter Double Hexagon 2I forgot to invert the algorithm. This has been corrected and 2 more moves have been cancelled. I guess Per's approach to the previous pattern could be applied to this one too Edges: U F' R' MF' R' F' R MF R' F2 U' ML2 U F' R2 F U' ML2 B MU L' MU' B' MU B L B SD' B' U' SB D MB2 D' SB' U B SD TB2 MU' Centers MU2 R' MU MR MU' R MU MR' MU' F MU' MF' MB' MU F' MU' MB MF MU' Double Hexagon 2 (56 btm)


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perfredlund

Post subject: Re: Patterns Posted: Sat Jul 07, 2012 4:10 am 

Joined: Fri May 06, 2005 10:13 am Location: Norway

Yet another hexagon pattern variety: Double Hexagon 3 (54 btm).A little bit tricky to avoid center side effects. But basically made up from previously published stuff Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy
Last edited by perfredlund on Sun Jul 08, 2012 1:25 pm, edited 1 time in total.


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perfredlund

Post subject: Re: Patterns Posted: Sun Jul 08, 2012 12:45 pm 

Joined: Fri May 06, 2005 10:13 am Location: Norway

Some more hexagon versions: Fat Hexagon (26 btm):Single Hexagon (25 btm).And an improved previously posted version: (this one is simply the first 2 combined ) Double Hexagon 2 (50 btm).There are many more possibilities, combining many axes of rotation  but i find that too tedious and not really interesting Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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perfredlund

Post subject: Re: Patterns Posted: Mon Jul 09, 2012 4:12 pm 

Joined: Fri May 06, 2005 10:13 am Location: Norway

Fat Hexagon (order 3) (21 btm).step1: U B2 WR2 L WF WR2 D WF D L B2 U (edges) step2: U F2 L2 D NR NB NR NB D L2 F2 U (centers) I could not resist this easy version (some insertion might improve this ... Glazik???) Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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glazik

Post subject: Re: Patterns Posted: Wed Jul 11, 2012 5:57 am 

Joined: Wed Oct 12, 2011 12:54 pm

Hi Per, Some algorithms of hexagon patterns have been improved. A shorter version of that of your last post couldn't be found though. Double Hexagon 3U D R2 B WU2 R' WU2 R B' R2 D' U' U2 B2 B2 R2 MU2 F2 MU2 TF2 MU2 TF2 R2 F2 R2 F2 B2 MF MD U MF' MD MF U' MF' MR' MD' MR MD' B2 U2 TU MR' B2 MR (TR' F2 TR MB TR' F2 TR MB') TF MR' B2 MR TF' TU' Double Hexagon 3 (53 btm)Single HexagonR' MU F2 MU' MB' MU F2 MU' MB B F MR U' MR' U B' L' U' MR U MR' L F' R Single Hexagon (23 btm)Double Hexagon 2R2 F2 MR2 U2 MR2 TU2 MR2 TU2 F2 U2 F2 U2 D2 MU ML R MU' ML MU R' MU' MF' ML' MF ML' D2 R2 R' MU F2 MU' MB' MU F2 MU' MB B F MR U' MR' U B' L' U' MR U MR' L F' R Double Hexagon 2 (48 btm)


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pytlivyj_1

Post subject: Patterns Posted: Wed Jul 11, 2012 11:07 am 

Joined: Tue Mar 24, 2009 12:52 pm

Large mezon on Bipolar Cube: If to put beside both kinds from opposite corners, they look as reflection in a mirror each other! Such interesting property of a puzzle.


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perfredlund

Post subject: Re: Patterns Posted: Tue Jul 17, 2012 2:51 pm 

Joined: Fri May 06, 2005 10:13 am Location: Norway

Fat Hexagon (order 6) (45 btm).Breakdown: 1. F L2 WU2 D WR WU2 B WR B D L2 F (edges, 3x3 style)) 2. F2 NR2 U2 NR2 TU2 NR2 NU2 F2 (last 2 edges  "parity") 3. NR2 ND NR U2 NR ND NR U2 NR (centers) 4. ND L2 ND NR ND L2 ND NR ND2 (more centers) 5. ND2 NU NL NU L NU NL NU L ND2 (final 2 centers) There should be room for plenty improvement Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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glazik

Post subject: Re: Patterns Posted: Wed Jul 18, 2012 3:32 am 

Joined: Wed Oct 12, 2011 12:54 pm

The algorithm of centers has been shortened. Further improvement is still feasible. Fat Hexagon (Order 6)Centers (composition of 3cycles): F2 U2 R2 [MU', MR] R' [MF2, R' MB' R] R R2 U2 F2 Fat Hexagon (Order 6) (32 btm)


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perfredlund

Post subject: Re: Patterns Posted: Wed Jul 18, 2012 3:35 pm 

Joined: Fri May 06, 2005 10:13 am Location: Norway

glazik wrote: The algorithm of centers has been shortened. Further improvement is still feasible. Fat Hexagon (Order 6)Centers (composition of 3cycles): F2 U2 R2 [MU', MR] R' [MF2, R' MB' R] R R2 U2 F2 Fat Hexagon (Order 6) (32 btm)This should be darn close to optimal. Nice work indeed EDIT: I found an alternative way to do the centers: 1. F2 U2 NU NR NU NR U2 F2 2. R2 ND NR2 ND R2 ND NR2 ND Fat Hexagon (Order 6) (32 btm).Less cancelled turns, but still resulting in 32 turns for the pattern And also i guess it's easier to optimise this one, with some insertion Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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glazik

Post subject: Re: Patterns Posted: Mon Jul 23, 2012 11:00 am 

Joined: Wed Oct 12, 2011 12:54 pm

perfredlund wrote: glazik wrote: The algorithm of centers has been shortened. Further improvement is still feasible. Fat Hexagon (Order 6)Centers (composition of 3cycles): F2 U2 R2 [MU', MR] R' [MF2, R' MB' R] R R2 U2 F2 Fat Hexagon (Order 6) (32 btm)This should be darn close to optimal. Nice work indeed EDIT: I found an alternative way to do the centers: 1. F2 U2 NU NR NU NR U2 F2 2. R2 ND NR2 ND R2 ND NR2 ND Fat Hexagon (Order 6) (32 btm).Less cancelled turns, but still resulting in 32 turns for the pattern And also i guess it's easier to optimise this one, with some insertion Per @ Per It appears that two centers located on faces R and L should be swapped. Maybe you could correct the alg. I think shorter algorithms could be found by searching directly for short 6cycles of edge pairs, although such a direct search for even cycles doesn't seem quite obvious. Here is an example of a 8move alg: [WR, U R B] Apart from 6cycles, 4cycles of pairs of edges or centers may also give simple patterns: Serpentine (Order 4)WU' WR' MF WU WR2 WU MF' WR' MR2 MU2 MR2 WF2 MU' WF2 MU' Serpentine (Order 4) (15 btm)Bridge(Order 4)WU' WR' MF WU WR2 WU MF' WR' SR2 MR2 MU2 MR2 WF2 MU' WF2 MU' SR2 Bridge (Order 4) (17 btm)


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perfredlund

Post subject: Re: Patterns Posted: Wed Jul 25, 2012 7:46 am 

Joined: Fri May 06, 2005 10:13 am Location: Norway

Hi Yes i noticed i made a mistake in my last post. I was gonna post a correction once i had a solution equalling or improving 32 turns. So far, no luck Maybe i will sticker the centres for some serious hunting later I improved the Serpentine (Order 4) (8 btm).And the Bridge (Order4) (13 btm).Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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glazik

Post subject: Re: Patterns Posted: Sat Jul 28, 2012 5:24 am 

Joined: Wed Oct 12, 2011 12:54 pm

Hi Per, Fat Hexagon (Order 6)No shorter algorithm could be found for edges BridgeThe algorithm can be improved by insertion of (MF2 MD2 MF2 MD2) into (WF2 MU WU2 MR2 WU2 MR2 MU' WF2 WU) MB2 MU2 MF2 MD2 MU MR2 WU2 MR2 MU' WF2 WU Bridge (11 btm)Fat Anaconda (Order 6)By reusing the algorithm of edges of the Fat Hexagon, a pattern of order 6 can be obtained (not yet optimized, though): 6 wide edges: F L2 WU2 D' WR WU2 B WR B' D L2 F MR2 U2 MR2 TU2 MR2 MU2 F2 6 big dots: MF2 WF WR2 MF2 WU' WR2 WF' WU F L2 WU2 D' WR WU2 B WR B' D L2 F MR2 U2 MR2 TU2 MR2 MU2 TF2 WF WR2 MF2 WU' WR2 WF' WU Fat Anaconda (Order 6) (26 btm)


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perfredlund

Post subject: Re: Patterns Posted: Sun Jul 29, 2012 2:54 pm 

Joined: Fri May 06, 2005 10:13 am Location: Norway

Yet another hexagon pattern, this time on 6x6x6. Double Hexagon 6x6x6 (order 3) (45 btm).Breakdown: 1. R L B2 U VL U2 VL U NF VD NF VD VF ND VF ND U VL U2 VL U B2 L R (centers) 2. R N3U F U2 F N3U N3D F U2 F N3D R (edges) 3. R N3B U F2 U N3B N3F U F2 U N3F R (final edges) I will explain part 1. First i do the dots with 2 overlapping bar 3cycles ([NF,VD] + [VF,ND]). I conjugate this with U VL U2 VL U first to make the dots on U,R,F faces cycle the correct way. Then i conjugate further with R L B2 U2 to finalise center positions 3 turns cancel out (as planned ) Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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glazik

Post subject: Re: Patterns Posted: Mon Jul 30, 2012 1:50 am 

Joined: Wed Oct 12, 2011 12:54 pm

This is a very interesting way of conjugating centers in just 2 phases A gain of 2 moves can be obtained by shortening the first setup phase, if (U VL' U2 VL U) is replaced with (VB' R2 VB U2) to give: (R L B2) (VB' R2 VB U2) (NF VD NF' VD' VF ND VF' ND') (U2 VB' R2 VB) (B2 L' R') Double Hexagon (Order 3) (6x6x6 Cube) (43 btm)The following is a list of new/alternate/improved algorithms of Big Dots (4x4x4 cubes) that could be added to Walter's website: (2c) (d,u) SR2 MF2 SR2 MB2 (4 m) (2c)(2c) (d,u) (b,f) WR WU2 WR' WU2 (4 m) (l,r) (b,f) SR2 WU SR2 WU (4 m) (b,d) (u,f) MR SU2 MR' ML' SU2 ML (6 m) (2c)(2c)(2c) (d,u) (l,r) (b,f) MR2 WU2 MR2 WF WU2 WF' (6 m) (b,u) (l,r) (d,f) MR WU2 WR' WF WU2 WF' ML' (7 m) (2c)(3c) (d,r) (l,u,b) WR WU WR' MD WR U2 WR' MU' MD' WR U2 WR' MD (13 m) (5c) (u,d,f,b,l) WR MD' R2 MD MU R2 MD' WR' MD R2 MD' MU' R2 MD (14 m) (r,b,l,f) MD' WF2 MD2 WR2 MD WF2 MD2 WR2 (r,u) MF WU' B2 WU MB' MF' WU' B2 WU MB (r,b,l,f)(r,u) = (r,b,l,f,u) = (u,r,b,l,f) MD' WF2 MD2 WR2 MD WF2 MD2 WR2 MF WU' B2 WU MB' MF' WU' B2 WU MB (18 m) (6c) (u,l,f,d,r,b) MB2 WU2 MB2 WB' WU' WB WU' (7 m)


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perfredlund

Post subject: Re: Patterns Posted: Tue Jul 31, 2012 7:18 am 

Joined: Fri May 06, 2005 10:13 am Location: Norway

Slight improvement: Double Hexagon (6x6x6) (42 btm).Primary setup: VU F2 VU2 R2 VU Center cycles: [VU , NB] and [NU , VB] etc etc .... Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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perfredlund

Post subject: Re: Patterns Posted: Tue Jul 31, 2012 8:22 am 

Joined: Fri May 06, 2005 10:13 am Location: Norway

And another version based on same setup turns: Wide Double Hexagons (6x6x6) (47 btm).This time doing 3 center cycles: [NU , N4B] , [N3U , N3B] and [N4U , NB]. Cheers Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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glazik

Post subject: Re: Patterns Posted: Tue Jul 31, 2012 12:25 pm 

Joined: Wed Oct 12, 2011 12:54 pm


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perfredlund

Post subject: Re: Patterns Posted: Wed Aug 01, 2012 6:21 am 

Joined: Fri May 06, 2005 10:13 am Location: Norway

Good job Glazik Her is another version: Fat Double Hexagon (6x6x6) (47 btm).Decomposition should be familiar Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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perfredlund

Post subject: Re: Patterns Posted: Wed Aug 01, 2012 10:50 am 

Joined: Fri May 06, 2005 10:13 am Location: Norway


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glazik

Post subject: Re: Patterns Posted: Thu Aug 02, 2012 7:25 am 

Joined: Wed Oct 12, 2011 12:54 pm

Double HexagonBy replacing setup (D2 VU F2 VU2 R2 VU) with (VD R2 T3D2 F2) a 2move gain can be obtained Double Hexagon (6x6x6) (40 btm)Big Dots (4x4x4)Here is another (unoptimized) algorithm: T3R2 D2 MB' SU2 MF U2 R2 MF WR2 MF' Big Dots (l,r,d,u) (4x4x4) (10 btm)As for Rings, the minimum set of cycles is 33 for Big Dots or Zeros: just too many cases but a few could still be considered


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perfredlund

Post subject: Re: Patterns Posted: Thu Aug 02, 2012 8:08 am 

Joined: Fri May 06, 2005 10:13 am Location: Norway

Excellent setup Glazik! I guess shorter than 40 would be hard to beat Here is a new pattern: Double Fat Triangle (38 btm).Other triangle patterns like this can surely be found Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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glazik

Post subject: Re: Patterns Posted: Fri Aug 03, 2012 12:21 pm 

Joined: Wed Oct 12, 2011 12:54 pm

perfredlund wrote: Excellent setup Glazik! I guess shorter than 40 would be hard to beat Here is a new pattern: Double Fat Triangle (38 btm).Other triangle patterns like this can surely be found Per Thanks, Per. Setups of less than 4 moves could not be found, so I think this 4mover may well be optimal The Double Fat Triangle pattern has been very slightly improved by replacing: 1 R (N3B U2 N3B' N3U' N3B U2 N3B' N3U) R' with R' (N3F N3D' F2 N3D N3F' N3D' F2 N3D) R 2 R' (V3F ND' F2 ND V3F' ND' F2 ND) R with R' N3D' (V3F ND' F2 ND V3F' ND' F2 ND) N3D R Double Fat Triangle (6x6x6) (37 btm)Here are simple variations of the 'Zero' pattern on a 6x6x6 cube: Four Zeros (f,b)(r,l)Insertion of 6mover (r,l) into (f,b): NR2 NF2 NU2 M2F2 V3U2 V3F2 V3R2 V3U2 M2R2 NU2 Four Zeros (f,b)(r,l) (10 btm)Four Chained ZerosNR2 NF2 NU2 M2F2 V3U2 V3F2 V3R2 V3U2 M2R2 NU2 N3U2 SF2 SL2 N3D2 SF2 SL2 Four Chained Zeros (15 btm)Two Chained HalfZeros B2 TR2 M2U NR2 WU' N3B2 ND' NU N3B2 R2 B2 N3D B F N3R N3L SF R2 SF' N3R' N3L' SF R2 F2 N3D' Two Chained HalfZeros (25 btm)Shorter versions can surely be found


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