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Deutsch 5D m-Symmetrie - entworfen von Reidenglish 5D m-symmetrie - by Reid
Corners Moved Straight - Edges Moved Straight 1Corners Moved Straight - Edges Moved Straight 2Corners Moved Straight - Edges Moved Diagonal P1Corners Moved Straight - Edges Moved Diagonal P2Corners Moved Straight - Edges Moved Diagonal M2Corners Moved Straight - Edges Moved Diagonal M1CMD1 EMS1CMD2 EMS1Corners Moved Diagonal 2 - Edges Moved Diagonal P1Corners Moved Diagonal 1 - Edges Moved Diagonal P1Corners Moved Positive - the long arm is the 'arrowpeak'Corners Moved Negative - the long arm is the 'arrowpeak'Corners Moved ParallelCorners Moved CrossEdges Moved Positive - the long arm is the 'arrowpeak'Edges Moved Negative - the long arm is the 'arrowpeak'Edges Moved ParallelEdges Moved CrossG-Permutation - Nose UpG-Permutation - Hand UpG-Permutation - Hand DownG-Permutation - Nose DownEdges Flipped NeighboursEdges Flipped OppositeEdges Flipped AllCorners Twisted StraightCorners Twisted NeighboursCorners Twisted DiagonalCorners Twisted PositiveCorners Twisted NegativeCorners Twisted RegularCorners Twisted IrregularCorners Moved Straight - Twisted StraightCorners Moved Straight - Twisted NeighboursCorners Moved Straight - Twisted DiagonalCorners Moved Straight - Twisted PositiveCorners Moved Straight - Twisted NegativeCorners Moved Straight - Twisted IrregularCorners Moved Straight - Twisted Regular
Twisting Corners & Flipping EdgesCorners Moved StraightCorners Moved DiagonalCorners Moved Positive - the long arm is the 'arrowpeak'Corners Moved Negative - the long arm is the 'arrowpeak'Corners Moved ParallelCorners Moved CrossFlipping EdgesEdges Moved StraightEdges Moved DiagonalEdges Moved Positive - the long arm is the 'arrowpeak'Edges Moved Negative - the long arm is the 'arrowpeak'Edges Moved ParallelEdges Moved Crossbest browser - Bester Browsercolor distribution - Farbverteilung
patterns by opposite swap - Muster durch gegenseitigen Tauschpattern index - Muster Indexpatterns by two axis swap - Muster durch 2-Achsen-Tauschpattern index - Muster Indexpatterns on two hemispheres by 1 axis cycle - Muster auf 2 Orientierungen, 1 Achsepattern index - Muster Index4 site cycle by 1 axis - Drehung von 4 Seiten durch 1 Achsepattern index - Muster Indexcycle of 6 sites by 1 axis - Drehung von 6 Seiten um 1 Achsepattern index - Muster Indexcheating swaps - betrügerisches Tauschenpattern index - Muster Indexpatterns by illegal swap - Muster durch illegalen Tauschpattern index - Muster Indexcollections - Sammlungenpattern index - Muster IndexDeclinations - Deklinationenpattern index - Muster IndexPrinting those Patterns
cheating swaps - betrügerisches Tauschen7D - odds / unregelmäßigepattern index - Muster Index7D - bars / Balkenpattern index - Muster Index7D - letters / Buchstabenpattern index - Muster Index7D - odds / unregelmäßigepattern index - Muster Index7D - flips of edges / Wendungen von Kantenpattern index - Muster Index7D - twists of corners / Eckendreherpattern index - Muster Indexirregular 3 bars outside - 3 irreguläre Außenbalkenpattern index - Muster Indexbs1 - flipping one edge by handpattern index - Muster Indexbs1 - flipping one edge by handpattern index - Muster Indexbs1 - flipping one edge by handpattern index - Muster Indexpattern index - Muster Index
AT-Symmetrie - by Reidpattern index - Muster IndexE-Symmetrie - by Reidpattern index - Muster IndexH-Symmetrie - by Reidpattern index - Muster IndexM-Symmetrie - by Reidpattern index - Muster IndexT-Symmetrie - by Reidpattern index - Muster IndexX-Symmetrie - by Reidpattern index - Muster IndexPatterns created by Reidpattern index - Muster Index
e-symm00
m-symm00m-symm00 back - m-symm00 hintenR'U²BL'FU'BDFe'LD²F'RB'DF'U'B'e'
R' U² B L' F U' B D F U D' L D² F' R B' D F' U' B' U D' (20,24)
UR²F'RD'LB'RU'ReF'UF'U'aBL'F'aD'L'
U R² F' R D' L B' R U' R U' D F' U F' U' D' B L' F' B' D' L' (20,24)
e'RFU'aLD'FRU'RU'aFU'FLB'UF'aLB'
U D' R F U' D' L D' F R U' R U' D' F U' F L B' U F' B' L B'(21,24)
e'RF'DL'BL'U'R'D'B'eL'FD'RB'RULDB
U D' R F' D L' B L' U' R' D' B' U' D L' F D' R B' R U L D B (22,24)
UR²FaRB²RU²LB²RU'aR²FmB²U²F²
U R² F B R B² R U² L B² R U' D' R² F R' L B² U² F² (17,28)
UR²FaRB²RU²LB²RU'aR²FD²B²U²lR'
U R² F B R B² R U² L B² R U' D' R² F D² B² U² R' L (17,29)
               
  english discussion about mentioned sequences (back to top)   deutsche Erörterung von Zugfolgen (zurück nach oben)  
   
These are all minimal maneuvers, up to cyclic shifting, inversion, and conjugation by symmetries of the cube. Dik Winter [8] was the first to find a 20f maneuver. Minimality of the 20f maneuver was first shown in [6]. The first known 24q maneuver (the (24q, 22f) maneuver) was found in [5]. Mark Longridge [4] notes that it has an interesting type of symmetry, namely that it is equivalent to iself under a cyclic shift by 12q and a cube symmetry. The second (24q, 24f) maneuver has a similar kind of symmetry. It was first shown in [7] that superflip requires at least 22 quarter turns. Jerry Bryan [1] was the first to show minimality of a 24q maneuver.

Reid

 
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Dies sind alle minimalen Operationen, bis hin zu Kreistausch, Umkehrung und Verknüpfungen der Symmetrien des Würfels. Dik Winter [8] war der erste, dem es zukam, ein 20f-Manöver zu finden. Die Minimalität des 20f_Manövers wurde zuerst in [6] gezeigt. Die erste bekannte 24q-Operation wurde in [5] gefunden. Mark Longridge bemerkt, daß es eine interessante Art von Symmetrie hat, namentlich zu sich selbst unter einem Kreistausch von 12q und einer Würfel-Symmetrie. Das zweite (24q, 24f) Manöver hat eine ähnliche Art von Symmetrie. Dies wurde zuerst in [7] gezeigt, daß der superflip mindestens 22q-Zöge benötigt. Jerry Bryan [1] war der erste, der dieses Minimum an 24q zeigte

Reid

   
00/00/2008 00.00.2008
         
             
m-symm01m-symm01 back - m-symm01 hintene''s²m''
U² D² F² B² R² L² (6,12)
se''m''s
F B' U² D² R² L² F B' (4,12)
sesese
F B' U' D F B' U' D F B' U' D (6,12)
               
  english discussion about mentioned sequences (back to top)   deutsche Erörterung von Zugfolgen (zurück nach oben)  
   
These are all minimal maneuvers, up to symmetries of the cube. (Each maneuver is equivalent to its inverse under symmetry.) Dan Hoey [3] originally found the interesting (12q, 12f) maneuver.

Reid

 
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Dies sind alles Minimal-Operationen, bis hin zu den Symmetrien des Würfels. (Jede Operation ist gleichartig zu ihrer Umkehrung unter Beachtung der Symmetrie) Dan Hoey [3] selber fand zuerst die interessante (12q, 12f) Manöver.

Reid

   
00/00/2008 00.00.2008
         
             
m-symm02m-symm02 back - m-symm02 hintenB'D'L'F'D's'Us'LR²'e'FLURD
B' D' L' F' D' F' B U F' B R² L U D' F L U R D (15,20)
F'U'B'R'Fm'D'm'e'L'e'FRBUF
F' U' B' R' F R L' D' R L' U D' L' U D' F R B U F (16,20)
B'R'F'U'Fm'D'm'e'L'e'FUFRB
B' R' F' U' F R L' D' R L' U D' L' U D' F U F R B (16,20)
B'R'B'D'FeL'em'U'm'FDBRB
B' R' B' D' F U' D L' U' D R L' U' R L' F D B R B (16,20)
RURBR'eFesDsR'B'R'U'R'
R U R B R' U' D F U' D F B' D F B' R' B' R' U' R' (16,20)
UaFm'sLD²RaF'aU'L²sU²L'
U D F R L' F B' L D² R L F' B' U' L² F B' U² L' (13,20)
UaF'aL'U²s'L²U'R'aF'es'D'L²
U D F' B' L' U² F' B L² U' R' L' F' U' D F' B D' L² (13,22)
U²RFUsL'D'sLBm'UD²'B'R'U²
U² R F U F B' L' D' F B' L B R L' U D² B' R' U² (15,22)
U²RFU²D'mF'L'sULsD'B'R'U²
U² R F U² D' R' L F' L' F B' U L F B' D' B' R' U² (15,22)
U²RD²sRU'L'UBRF²eB'R'F'DB'L²
U² R U² D² R U' L' U B R F² U' D B' R' F' D B' L² (18,24)
1 english discussion about mentioned sequences (back to top)
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deutsche Erörterung von Zugfolgen (zurück nach oben)  

M-symmetric positions

These are all minimal maneuvers, up to inversion and symmetries of the cube. Jerry Bryan [2] was the first to find the 20q maneuvers.

Reid


Zentralsymmetrische Positionen

Dies sind alle Minimal-Operationen, bis hin zu Umkehrung und Symmetrien des Würfels. Jerry Bryan [2] war der erste, der das 20q-Manöver fand.

Reid

   
     

References

[1] Jerry Bryan, Qturn Lengths of M-Symmetric Positions, cube-lovers e-mail, February 19, 1995.
[2] Jerry Bryan, Pons Asinorum Superflipped Halfway Positions (corrected), cube-lovers e-mail, February 20, 1995.
[3] Dan Hoey, Pons Asinorum -- Part 2: Pons in the Supergroup, cube-lovers e-mail, January 7, 1981.
[4] Mark Longridge, Superflip 24q, cube-lovers e-mail, January 19, 1995.
[5] michael reid, superflip, cube-lovers e-mail, January 10, 1995.
[6] michael reid, superflip requires 20 face turns, cube-lovers e-mail, January 18, 1995.
[7] michael reid, superflip in quarter turn metric, cube-lovers e-mail, January 20, 1995.
[8] Dik T. Winter, Kociemba's algorithm, cube-lovers e-mail, May 18, 1992.
Symmetric positions | Cube page | Home page | E-mail
     
   
   


 
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01/14/2009 14.01.2009
       

 

 

 

 

 

 

 

 

 

 

 

 

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