博文
Magic Dodecahedron (Megaminx)：编程玩五边形12面魔方
精选
|||
Magic Dodecahedron (Megaminx)：编程玩五边形12面魔方
Megaminx有12个5次轴，从空间分布看，和足球C60的5次轴一模一样，和谢赫德曼20面准晶体的5次轴一模一样。需要强调的是，C60和谢赫特曼的20面准晶体模型有只6个五次轴。
然而对于Megaminx，一个轴有两个“箭头”，因此，共有12个5次轴。我用W、A、B、C、D、E、S、H、G、F、N、M表示Megaminx的12个面，每个面上有个5次轴。
用计算机玩Megaminx，首先要有数学模型，然后是编程算法，最后是编程技巧。如果硬要归类的话，俺干的活，可以归类到几何代数学。
普通3阶魔方，可运动的小块有20个：8个角块和12个心块。
Megaminx，有50个可运动的小块：20个角块，30个边块。
Megaminx的12个面，可转动的角度有：72度、144度、216度、288度。用1、2、3、4分别表示72度、144度、216度、288度，对于只操作某个面，转动5之后，Megaminx就回复到原始状态。
如果你有个Megaminx，转动某个面，例如W面，容易验证：
(W1)5=I；(W2)5=I；(W3)5=I；(W4)5=I。
对于Rubik魔方，同样转动某面（W），结果如下：
(W1)4=I；(W2)2=I；(W3)4=I.
对于Megaminx，如果先转动W1面，再转动A1面，则有
(W1A1)63=I.
如果按照W1A1B1操作Megaminx，则有
(W1A1B1)351=I.
点群的魅力：正五边形12面魔方
建议用Mozilla Firefox或者InternetExplorer浏览器
"N represents the counting of twisting for the operation sequence"
"T represents the side of twisting currently"
"RC represents the angle of twisting currently"
"C represents the cyclic periodicity of employing the operation sequence"
"N=",1," T=","W"," RC=",2," C=",1
" W "
" W W "
" W W W "
" W W "
" W W W "
" D D D "," E E E "," A A A "," B B B "," C C C "
" A A "," B B "," C C "," D D "," E E "
" A A A "," B B B "," C C C "," D D D "," E E E "
" A A "," B B "," C C "," D D "," E E "
" A "," B "," C "," D "," E "
" S "
" S S "
" S S S "
" S S "
" S S S "
" H H H "," G G G "," F F F "," N N N "," M M M "
" H H "," G G "," F F "," N N "," M M "
" H H H "," G G G "," F F F "," N N N "," M M M "
" H H "," G G "," F F "," N N "," M M "
" H "," G "," F "," N "," M "
"N=",2," T=","W"," RC=",2," C=",2
" W "
" W W "
" W W W "
" W W "
" W W W "
" B B B "," C C C "," D D D "," E E E "," A A A "
" A A "," B B "," C C "," D D "," E E "
" A A A "," B B B "," C C C "," D D D "," E E E "
" A A "," B B "," C C "," D D "," E E "
" A "," B "," C "," D "," E "
" S "
" S S "
" S S S "
" S S "
" S S S "
" H H H "," G G G "," F F F "," N N N "," M M M "
" H H "," G G "," F F "," N N "," M M "
" H H H "," G G G "," F F F "," N N N "," M M M "
" H H "," G G "," F F "," N N "," M M "
" H "," G "," F "," N "," M "
"N=",3," T=","W"," RC=",2," C=",3
" W "
" W W "
" W W W "
" W W "
" W W W "
" E E E "," A A A "," B B B "," C C C "," D D D "
" A A "," B B "," C C "," D D "," E E "
" A A A "," B B B "," C C C "," D D D "," E E E "
" A A "," B B "," C C "," D D "," E E "
" A "," B "," C "," D "," E "
" S "
" S S "
" S S S "
" S S "
" S S S "
" H H H "," G G G "," F F F "," N N N "," M M M "
" H H "," G G "," F F "," N N "," M M "
" H H H "," G G G "," F F F "," N N N "," M M M "
" H H "," G G "," F F "," N N "," M M "
" H "," G "," F "," N "," M "
"N=",4," T=","W"," RC=",2," C=",4
" W "
" W W "
" W W W "
" W W "
" W W W "
" C C C "," D D D "," E E E "," A A A "," B B B "
" A A "," B B "," C C "," D D "," E E "
" A A A "," B B B "," C C C "," D D D "," E E E "
" A A "," B B "," C C "," D D "," E E "
" A "," B "," C "," D "," E "
" S "
" S S "
" S S S "
" S S "
" S S S "
" H H H "," G G G "," F F F "," N N N "," M M M "
" H H "," G G "," F F "," N N "," M M "
" H H H "," G G G "," F F F "," N N N "," M M M "
" H H "," G G "," F F "," N N "," M M "
" H "," G "," F "," N "," M "
"N=",5," T=","W"," RC=",2," C=",5
" W "
" W W "
" W W W "
" W W "
" W W W "
" A A A "," B B B "," C C C "," D D D "," E E E "
" A A "," B B "," C C "," D D "," E E "
" A A A "," B B B "," C C C "," D D D "," E E E "
" A A "," B B "," C C "," D D "," E E "
" A "," B "," C "," D "," E "
" S "
" S S "
" S S S "
" S S "
" S S S "
" H H H "," G G G "," F F F "," N N N "," M M M "
" H H "," G G "," F F "," N N "," M M "
" H H H "," G G G "," F F F "," N N N "," M M M "
" H H "," G G "," F F "," N N "," M M "
" H "," G "," F "," N "," M "
https://blog.sciencenet.cn/blog-2321-1084153.html
上一篇：白猫和黑猫 打起来了
下一篇：道法自然：鸟子爱财，取之有道
