MHB In how many ways can a cube with 8 different vertices be oriented?

[alexmahone]

My solution:

Imagine that we have 8 points in space which must be occupied by the vertices of the cube.
Let A be one of the points. Fix anyone of the vertices at A. This can be done in 8 ways.
We have 3 different choices for an adjacent point (say B) because each vertex of a cube is connected to 3 other vertices.
Once A and B (being adjacent points) are determined, the other points are automatically determined. (Is this true? If so, how would I prove it?)
So we have 8*3 = 24 orientations.

Is this correct?

 

[Evgeny.Makarov]

Yes, there are 24 cube rotations, or "physical symmetries", as they are called in this article.