三阶魔方公式的最大周期是多少？对应的公式是什么？ 第1页

                RubikMap                   =                   <|                             "U"                   ->                   Cycles         @         {{         1         ,                   3         ,                   8         ,                   6         },                   {         2         ,                   5         ,                   7         ,                   4         },                   {         9         ,                   33         ,                   25         ,                   17         },                   {         10         ,                   34         ,                   26         ,                   18         },                   {         11         ,                   35         ,                   27         ,                   19         }},                             "D"                   ->                   Cycles         @         {{         14         ,                   22         ,                   30         ,                   38         },                   {         15         ,                   23         ,                   31         ,                   39         },                   {         16         ,                   24         ,                   32         ,                   40         },                   {         41         ,                   43         ,                   48         ,                   46         },                   {         42         ,                   45         ,                   47         ,                   44         }},                             "L"                   ->                   Cycles         @         {{         1         ,                   17         ,                   41         ,                   40         },                   {         4         ,                   20         ,                   44         ,                   37         },                   {         6         ,                   22         ,                   46         ,                   35         },                   {         9         ,                   11         ,                   16         ,                   14         },                   {         10         ,                   13         ,                   15         ,                   12         }},                             "R"                   ->                   Cycles         @         {{         3         ,                   38         ,                   43         ,                   19         },                   {         5         ,                   36         ,                   45         ,                   21         },                   {         8         ,                   33         ,                   48         ,                   24         },                   {         25         ,                   27         ,                   32         ,                   30         },                   {         26         ,                   29         ,                   31         ,                   28         }},                             "B"                   ->                   Cycles         @         {{         1         ,                   14         ,                   48         ,                   27         },                   {         2         ,                   12         ,                   47         ,                   29         },                   {         3         ,                   9         ,                   46         ,                   32         },                   {         33         ,                   35         ,                   40         ,                   38         },                   {         34         ,                   37         ,                   39         ,                   36         }},                              "F"                   ->                   Cycles         @         {{         6         ,                   25         ,                   43         ,                   16         },                   {         7         ,                   28         ,                   42         ,                   13         },                   {         8         ,                   30         ,                   41         ,                   11         },                   {         17         ,                   19         ,                   24         ,                   22         },                   {         18         ,                   21         ,                   23         ,                   20         }}                            |>         ;                            RubikPeriod         [         input_String         ]                   :=                   Apply         [         LCM         ,                   Length                   /@                   First         @         RubikCycle         [         input         ]];                            RubikCycle         [         input_String         ]                   :=                   GeneralUtilities`         Scope         [                             (*doMap[O_String]:=RubikMap@O;*)                             (*doMap[inverse[O_]]:=InversePermutation[RubikMap@O];*)                             (*doMap[double[O_]]:=PermutationPower[RubikMap@O,2];*)                             (*sp={{a_,"'"}[RuleDelayed]inverse@a,{a_,"2"}[RuleDelayed]double@a};*)                             (*seq=SequenceReplace[StringPartition[StringDelete[ToUpperCase@input," "],1],sp];*)                             (*Apply[PermutationProduct,doMap/@seq]*)                             sp                   =                   {{         a_         ,                   "'"         }                   :>                   {         a         ,                   a         ,                   a         },                   {         a_         ,                   "2"         }                   :>                   {         a         ,                   a         }};                             seq                   =                   SequenceReplace         [         StringPartition         [         StringDelete         [         ToUpperCase         @         input         ,                   " "         ],                   1         ],                   sp         ];                             Apply         [         PermutationProduct         ,                   RubikMap                   /@                   Flatten         @         seq         ]                            ];                                      perm                   =                   RubikCycle         @         "RU2D'BD'"         ;                            Echo         [         Apply         [         LCM         ,                   Length                   /@                   First         @         perm         ],                   "Period: "         ];                            rules         [         cycle_         ]                   :=                   Thread         [         DirectedEdge         [         cycle         ,                   RotateLeft         [         cycle         ]]];                            Graph         [         Flatten         [         rules                   /@                   First         [         perm         ]],                   VertexLabels                   ->                   Placed         [         "Name"         ,                   Center         ],                   VertexSize                   ->                   0.6         ]