1) What coordinates of cubes for?

They may be used for first trick in tests:
placing two cubes in the same position.

2) Are there may be another tricks with coordinates data.

3) Besides unclear using of coordinates, the problem
is standard problen on groop of rotations of cube in space with 24 elems and searchig after maximal matching.

Clearness is taken.
1. Coordinates have no any importance.
2. Matching program may be standard.
3. Groop of rotations must be calculated
absolutely exactly of caurse.
For example I used the next matrix:
/ 1-left,2-right,3-top,4-forward,5-bottom,6- back
int A[24][6]={
1,2,3,4,5,6,
 1,2,4,5,6,3,
1,2,5,6,3,4,
1,2,6,3,4,5,
6,4,3,1,5,2,
2,1,3,6,5,4,
4,6,3,2,5,1,
3,5,2,4,1,6,
2,1,5,4,3,6,
5,3,1,4,2,6,
4,6,5,1,3,2,
6,4,5,2,3,1,
2,1,4,3,6,5,
2,1,6,5,4,3,
3,5,1,6,2,4,
5,3,2,6,1,4,
5,3,6,1,4,2,
4,6,2,5,1,3,
4,6,1,3,2,5,
3,5,4,1,6,2,
3,5,6,2,4,1,
6,4,1,5,2,3,
5,3,4,2,6,1,
6,4,2,3,1,5};

I don't see why you need this matrix. it's too easy to generate.