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Deutsch 5D h-Symmetrie - entworfen von Reidenglish 5D h-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
h-symm00h-symm00 back - h-symm00 hintenURs'U'aFeFLF'L'URDFURa
U R F' B U' D' F U' D F L F' L' U R D F U R L (16,20)
h-symm01h-symm01 back - h-symm01 hintenUR'BDBULDB'D²RU'FLFRDLF'L²
U R' B D B U L D B' D² R U' F L F R D L F' L² (20,22)
B'L²UaR²B'D²F²D'R²FaL²D'B²U²
B' L² U D R² B' D² F² D' R² F B L² D' B² U² (14,24)
h-symm02h-symm02 back - h-symm02 hintenD²L²B²D²sB²R²D²
D² L² B² U² D² B² R² D² (7,16)
h-symm03h-symm03 back - h-symm03 hintenUF'L's'URs'U'B'e'L'R²BU'
U F' L' F' B U R F' B U' B' U D' R² L' B U' (13,18)
h-symm04h-symm04 back - h-symm04 hintenUFaDRaU's²RaD'FaDRaDF'a
U F B D R L U' F² B² R L D' F B D R L D F' B' (13,22)
h-symm05h-symm05 back - h-symm05 hintenFLDFU'B²RFR'F'RFL²U'RDBR
F L D F U' B² R F R' F' R F L² U' R D B R (18,20)
h-symm05h-symm05 back - h-symm05 hintenB²LU²F'aU²R'F²L²F'U²R'aU²BR²
B² L U² F' B' U² R' F² L² F' U² R' L' U² B R² (14,24)
h-symm06h-symm06 back - h-symm06 hintenUFaU'RaUFaR²sD'FaU'RaD'R'a
U F B U' R L U F B R² L² D' F B U' R L D' R' L' (13,22)
h-symm09h-symm09 back - h-symm09 hinten
h-symm07h-symm07 back - h-symm07 hintenU²LUBDLUB'R'aF'DRUFDL'U²
U² L U B D L U B' R' L' F' D R U F D L' U² (17,20)
L'B²U'aB²R'U²L²UB²RaF²UR²U²
L' B² U' D' B² R' U² L² U B² R L F² U R² U² (14,24)
h-symm08h-symm08 back - h-symm08 hinten
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H-symmetric positions

These are the positions that are invariant under all symmetries producing an even permutation of long diagonals of the cube. There are 24 such positions; 4 have more symmetry, namely M-symmetry. The other 20 positions pair up into 10 patterns, as shown below. I have even calculated all minimal maneuvers, using my optimal cube solver.

Reid


H-symmetrische Stellungen

Hier sind alle Stellungen enthalten, die unter allen Symmetrien unveränderlich sind, die einen einfachen Tausch entlang der langen Diagonalen des Würfels beinhalten. Es gibt 24 solche Stellungen; 4 haben mehrere Symmetrien, namentlich die M-Symmetrie. Die anderen 20 Stellungen teilen sich in 10 Muster, wie hier angezeigt wird. Auch habe ich alle minimalen Operationen durch meinen optimal cube solver berechnen lassen.

Reid

   
     
References

[1] Herbert Kociemba, Close to God's Algorithm, Cubism For Fun 28 (April 1992) pp. 10-13.
[2] James Saxe, 16 qtw algs for CC and H patterns, cube-lovers e-mail, December 16, 1980.
[3] Dik T. Winter, Are we approaching God's algorithm?, cube-lovers e-mail, May 4, 1992.
[4] Dik T. Winter, Kociemba's algorithm, cube-lovers e-mail, May 17, 1992.
[5] Dik T. Winter, Re: Diameter of cube group?, cube-lovers e-mail, August 25, 1993.
     
   
               
01/14/2009 14.01.2009
       

 

 

 

 

 

 

 

 

 

 

 

 

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