“（伯恩赛德引理）设G是一个作用在有限集合X上的有限群，令N为轨道的个数，则
其中Fix(x)是被τ固定的x∈X的个数.“
*高等近世代数 Joseph J. Rotman P78
“设G是一个有限群，作用在集合X上。对每个g属于G令X^g表示X中在g作用下的不动元素。伯恩赛德引理断言轨道数（记作X/G）由如下公式给出：
从而轨道数（是一个自然数或无穷）等于被G中一个元素保持不动的点个数的平均值（故同样是自然数或无穷）。
使用三种颜色对立方体的面染色，旋转后相同的视为一种，染色方式总数可以由这个公式确定。选取一个定向，设X是这个定向立方体所有36种可能面染色组合，立方体的旋转群自然作用在X上。则X的两个元素属于同一轨道恰好是一个是另一个的旋转。旋转不同的染色数就是轨道数，可以通过数G的24个元素的不动集合的大小求出来 “
*百度伯恩赛德引理
这里把所有57种可能都算出来了，立方体大小是4*4*4
| 1 | 48 | 57 | |||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||
| 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | ||
| 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | ||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||
| ** | ** | ** | |||||||||||
| 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | ||
| 1 | 0 | 0 | 1 | 2 | 0 | 0 | 2 | 3 | 0 | 0 | 3 | ||
| 1 | 0 | 0 | 1 | 2 | 0 | 0 | 2 | 3 | 0 | 0 | 3 | ||
| 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | ||
| ** | ** | ** | |||||||||||
| 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | ||
| 1 | 0 | 0 | 1 | 2 | 0 | 0 | 2 | 3 | 0 | 0 | 3 | ||
| 1 | 0 | 0 | 1 | 2 | 0 | 0 | 2 | 3 | 0 | 0 | 3 | ||
| 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | ||
| ** | ** | ** | |||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||
| 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | ||
| 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | ||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||
| ***** | 6 | ***** | 6 | ***** | 6 | ||||||||
6个面颜色相同的有3种
| 2 | 3 | 32 | 49 | 47 | 56 | |||||||||||||||||||||||
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| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | |||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| ** | ** | ** | ** | ** | ** | |||||||||||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | |||||
| 1 | 0 | 0 | 2 | 1 | 0 | 0 | 3 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | |||||
| 1 | 0 | 0 | 2 | 1 | 0 | 0 | 3 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | |||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | |||||
| ** | ** | ** | ** | ** | ** | |||||||||||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | |||||
| 1 | 0 | 0 | 2 | 1 | 0 | 0 | 3 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | |||||
| 1 | 0 | 0 | 2 | 1 | 0 | 0 | 3 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | |||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | |||||
| ** | ** | ** | ** | ** | ** | |||||||||||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | |||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | |||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| ***** | 15 | ***** | 15 | ***** | 15 | ***** | 15 | ***** | 15 | ***** | 15 | |||||||||||||||||
6个面有2种颜色，2个颜色的比例是1/5的有6种
| 4 | 7 | 6 | 12 | |||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||
| 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 1 | 1 | 0 | 0 | 3 | 3 | 0 | |||
| 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 1 | 1 | 0 | 0 | 3 | 3 | 0 | |||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||
| ** | ** | ** | ** | |||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | |||
| 2 | 0 | 0 | 2 | 1 | 0 | 0 | 2 | 3 | 0 | 0 | 3 | 1 | 0 | 0 | 3 | |||
| 2 | 0 | 0 | 2 | 1 | 0 | 0 | 2 | 3 | 0 | 0 | 3 | 1 | 0 | 0 | 3 | |||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | |||
| ** | ** | ** | ** | |||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | |||
| 2 | 0 | 0 | 2 | 1 | 0 | 0 | 2 | 3 | 0 | 0 | 3 | 1 | 0 | 0 | 3 | |||
| 2 | 0 | 0 | 2 | 1 | 0 | 0 | 2 | 3 | 0 | 0 | 3 | 1 | 0 | 0 | 3 | |||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | |||
| ** | ** | ** | ** | |||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | |||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | |||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||
| ***** | 24 | ***** | 24 | ***** | 24 | ***** | 24 | |||||||||||
| 16 | 24 | 50 | 51 | ||||||||||||||||||||||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||||||||||||||||||||
| 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | ||||||||||||||||||||||
| 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | ||||||||||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||||||||||||||||||||
| ** | ** | ** | ** | ||||||||||||||||||||||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | ||||||||||||||||||||||
| 2 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | ||||||||||||||||||||||
| 2 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | ||||||||||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | ||||||||||||||||||||||
| ** | ** | ** | ** | ||||||||||||||||||||||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | ||||||||||||||||||||||
| 2 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | ||||||||||||||||||||||
| 2 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | ||||||||||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | ||||||||||||||||||||||
| ** | ** | ** | ** | ||||||||||||||||||||||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||||||||||||||||||||
| 0 | 2 | 2 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | ||||||||||||||||||||||
| 0 | 2 | 2 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | ||||||||||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||||||||||||||||||||
| ***** | 24 | ***** | 24 | ***** | 24 | ***** | 24 | ||||||||||||||||||||||||||||||
| 21 | 41 | 53 | 55 | ||||||||||||||||||||||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||||||||||||||||||||
| 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | ||||||||||||||||||||||
| 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | ||||||||||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||||||||||||||||||||
| ** | ** | ** | ** | ||||||||||||||||||||||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | ||||||||||||||||||||||
| 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | ||||||||||||||||||||||
| 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | ||||||||||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | ||||||||||||||||||||||
| ** | ** | ** | ** | ||||||||||||||||||||||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | ||||||||||||||||||||||
| 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | ||||||||||||||||||||||
| 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | ||||||||||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | ||||||||||||||||||||||
| ** | ** | ** | ** | ||||||||||||||||||||||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||||||||||||||||||||
| 0 | 3 | 3 | 0 | 0 | 1 | 1 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | ||||||||||||||||||||||
| 0 | 3 | 3 | 0 | 0 | 1 | 1 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | ||||||||||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||||||||||||||||||||
| ***** | 24 | ***** | 24 | ***** | 24 | ***** | 24 | ||||||||||||||||||||||||||||||
6个面有2种颜色，两种颜色比例是2/4的有12种
| 5 | 8 | 42 | 33 | 37 | 46 | |||||||||||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | |||||
| 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | |||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| ** | ** | ** | ** | ** | ** | |||||||||||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | |||||
| 2 | 0 | 0 | 3 | 1 | 0 | 0 | 3 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | |||||
| 2 | 0 | 0 | 3 | 1 | 0 | 0 | 3 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | |||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | |||||
| ** | ** | ** | ** | ** | ** | |||||||||||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | |||||
| 2 | 0 | 0 | 3 | 1 | 0 | 0 | 3 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | |||||
| 2 | 0 | 0 | 3 | 1 | 0 | 0 | 3 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | |||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | |||||
| ** | ** | ** | ** | ** | ** | |||||||||||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | |||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | |||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| ***** | 114 | ***** | 114 | ***** | 114 | ***** | 114 | ***** | 114 | ***** | 114 | |||||||||||||||||
6个面有3种颜色，3种颜色的比例是1：1：4的有6个
| 9 | 22 | 15 | 38 | 52 | 54 | |||||||||||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | |||||
| 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | |||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| ** | ** | ** | ** | ** | ** | |||||||||||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | |||||
| 2 | 0 | 0 | 2 | 1 | 0 | 0 | 2 | 3 | 0 | 0 | 3 | 1 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | |||||
| 2 | 0 | 0 | 2 | 1 | 0 | 0 | 2 | 3 | 0 | 0 | 3 | 1 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | |||||
| 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 1 | 1 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | |||||
| ** | ** | ** | ** | ** | ** | |||||||||||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | |||||
| 2 | 0 | 0 | 2 | 1 | 0 | 0 | 2 | 3 | 0 | 0 | 3 | 1 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | |||||
| 2 | 0 | 0 | 2 | 1 | 0 | 0 | 2 | 3 | 0 | 0 | 3 | 1 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | |||||
| 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 1 | 1 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | |||||
| ** | ** | ** | ** | ** | ** | |||||||||||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | |||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | |||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| ***** | 33 | ***** | 33 | ***** | 33 | ***** | 33 | ***** | 33 | ***** | 33 | |||||||||||||||||
6个面只有2种颜色，两种颜色比例是3/3，有6个
| 13 | 10 | 11 | 14 | 23 | 27 | |||||||||||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | |||||
| 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | |||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| ** | ** | ** | ** | ** | ** | |||||||||||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | |||||
| 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | 1 | 0 | 0 | 3 | 1 | 0 | 0 | 3 | |||||
| 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | 1 | 0 | 0 | 3 | 1 | 0 | 0 | 3 | |||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | |||||
| ** | ** | ** | ** | ** | ** | |||||||||||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | |||||
| 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | 1 | 0 | 0 | 3 | 1 | 0 | 0 | 3 | |||||
| 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | 1 | 0 | 0 | 3 | 1 | 0 | 0 | 3 | |||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | |||||
| ** | ** | ** | ** | ** | ** | |||||||||||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | |||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | |||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| ***** | 123 | ***** | 123 | ***** | 123 | ***** | 123 | ***** | 123 | ***** | 123 | |||||||||||||||||
| 28 | 17 | 34 | 43 | 25 | 35 | |||||||||||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | |||||
| 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | |||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| ** | ** | ** | ** | ** | ** | |||||||||||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | |||||
| 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | |||||
| 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | |||||
| 0 | 2 | 2 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | |||||
| ** | ** | ** | ** | ** | ** | |||||||||||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | |||||
| 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | |||||
| 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | |||||
| 0 | 2 | 2 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | |||||
| ** | ** | ** | ** | ** | ** | |||||||||||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | |||||
| 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | |||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| ***** | 123 | ***** | 123 | ***** | 123 | ***** | 123 | ***** | 123 | ***** | 123 | |||||||||||||||||
| 20 | 31 | 36 | 44 | 45 | 40 | |||||||||||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | |||||
| 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | |||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| ** | ** | ** | ** | ** | ** | |||||||||||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | |||||
| 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | |||||
| 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | |||||
| 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | |||||
| ** | ** | ** | ** | ** | ** | |||||||||||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | |||||
| 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | |||||
| 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | |||||
| 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | |||||
| ** | ** | ** | ** | ** | ** | |||||||||||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| 0 | 2 | 2 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 1 | 1 | 0 | |||||
| 0 | 2 | 2 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 1 | 1 | 0 | |||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| ***** | 123 | ***** | 123 | ***** | 123 | ***** | 123 | ***** | 123 | ***** | 123 | |||||||||||||||||
6个面有3种颜色，3个颜色比例是1：2：3的有18个
| 18 | 19 | 26 | 39 | 29 | 30 | |||||||||||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | |||||
| 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 3 | 0 | |||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| ** | ** | ** | ** | ** | ** | |||||||||||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | |||||
| 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | |||||
| 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | |||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | |||||
| ** | ** | ** | ** | ** | ** | |||||||||||||||||||||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | |||||
| 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | |||||
| 3 | 0 | 0 | 3 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 3 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | |||||
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 2 | 2 | 0 | 0 | 3 | 3 | 0 | 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | |||||
| ** | ** | ** | ** | ** | ** | |||||||||||||||||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | |||||
| 0 | 2 | 2 | 0 | 0 | 2 | 2 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | |||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |||||
| ***** | 222 | ***** | 222 | ***** | 222 | ***** | 222 | ***** | 222 | ***** | 222 | |||||||||||||||||
6个面有3种颜色，3种颜色比例是2：2：2的有6个。
| 数量 | 比例 |
| 3 | 6 |
| 6 | 15 |
| 12 | 24 |
| 6 | 114 |
| 6 | 33 |
| 18 | 123 |
| 6 | 222 |
共有57个不同的染色方式。
