# The Group of Rotations of the Cube

The Group of Rotations of the Cube

Consider a particular representation, , of on that preserves a cube centered at the origin, with faces orthogonal to the axes. By examining the action of elements of the group on the cube, both singly and in composition with other elements, you can see that is isomorphic to the group of rotations of the cube. The brightest cube is fixed and the next two cubes show the actions of and . The axes of rotation are shown in gray. The thickest axis represents .

ρ

S

4

3

S

4

B

AB

AB