Painting a 2x2x2 Cube

Suppose you have a 2×2×22 \times 2 \times 2 cube and you can color each of the 24 little squares one of four\color{#D61F06}\text{f}\color{#20A900} \text{o}\color{#3D99F6} \text{u}\color{#EC7300} \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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