题目189：用三种颜色着色三角形

欧拉计划

Tri-colouring a triangular grid

Consider the following configuration of 64 triangles:

We wish to colour the interior of each triangle with one of three colours: red, green or blue, so that no two neighbouring triangles have the same colour. Such a colouring shall be called valid. Here, two triangles are said to be neighbouring if they share an edge.
Note: if they only share a vertex, then they are not neighbours.

For example, here is a valid colouring of the above grid:

A colouring C' which is obtained from a colouring C by rotation or reflection is considered distinct from C unless the two are identical.

How many distinct valid colourings are there for the above configuration?

题目：

考虑如下64个三角形的组合：

我们希望将其中的每个三角形用红，绿，蓝之中的一种颜色着色，要求任意相邻的两个三角形具有不同的颜色。符合如上条件的着色为有效着色。两个三角形相邻的条件为它们有共同的边。

注意：如果两个三角形只共享一个顶点，则不算相邻。

例如，下面是上述格子的一种有效着色：

如果一种着色 C 旋转或镜面反射之后得到的着色  C' 与原来的着色不同，也算作不同的着色。


问上面的格子有多少种有效着色？