Painting a 2x2x2 Cube

Suppose you have a \(2 \times 2 \times 2\) cube and you can color each of the 24 little squares one of \(\color{Red}\text{f}\color{Green} \text{o}\color{Blue} \text{u}\color{Orange} \text{r}\) colors.

Is it possible to paint the cube so that the following holds true?

  • None of the 3 squares meeting at a corner are the same color.
  • None of the 4 squares meeting along an edge are the same color.
  • None of the 4 squares on any face are the same color.
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