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五魔方(Megaminx)的数学模型
https://www.youtube.com/channel/UCeNplibjHdednjiqUY4IcEg
如图1安放五魔方在笛卡儿坐标系:把1个五次轴置于[z]方向,把1个二次轴位于[y]方向。X轴的露头点既不位于顶点,也不位于棱边中点,因此其他的轴都是“歪轴”,这些的“歪轴”的操作矩阵是很难用肉眼一下看出来的。
对于描述五魔方(Megaminx)的转动,只需要五次轴的转动矩阵。所有的关于五魔方的转动矩阵,都可以在Ih点群中找到。需要强调的是,这些转动矩阵的表达形式和笛卡儿坐标系有关,即12面体在笛卡儿坐标系的不同安放,对应的转动矩阵是不同的。五魔方的定面(W)和底面(S)的转动,可以用如下矩阵描述,对于W面,转动方向满足右手定则,对于S面,转动方向,按照左手定则。
为了简单,我用文本输出表示魔方状态,对应关系如图2所示。
下面的五魔方被搅乱了,但是仅局限于顶层,复位操作见其后。
"Nrepresents the counting of twisting for the operation sequence"
"Trepresents the side of twisting currently"
"RCrepresents the angle of twisting currently"
"InCartesian Coordinate System, ","The Operation Sequence is "
"B",4,";","W",2,";","E",1,";","W",3,";","B",1,";","W",2,";","E",4,";","W",3,";",
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