Number of Rotations of a unit cube

Question

Let $C $ be the unit cube $[-1,1]^3 \subseteq \mathbb R^3$.How many rotations are there in $\mathbb R^3$ which take $\mathbb C$ to itself?

Please help me to visualize this.

Answer 1

Fix an edge of the cube. You can superimpose it on any other edge of the cube by a rotation (movement) and in two different ways. Therefore, there are $2 \times 12 = 24$ rotations.

This works for any regular polyhedron: the number of rotations $= 2 \times$ number of edges, while the number of isometries $= 4 \times$ number of edges.