I have been trying to work out the number of possible unique combinations of 4 cubes where they can be rotated on any axis.
So for example if all the faces of all the cubes where unique across the entire set this would cover all possible combinations of each side.
I thought it would be
$ 6! * 4^3 $
= 46080
But I'm not sure if that is even close to being correct. Help much appreciated as this is one of my weaker parts of maths.
I am only interested in the combinations of sides and the order of the cubes does not matter
Each cube has $24$ orientations. You can select the top face $6$ ways, then the front face in $4$ ways and the orientation is specified. Given four cubes, you then have $24^4=331776$ orientations. Is this what you were looking for?