The two sliders can be used to select elements

and

from

. These elements are shown in cycle form, as is their composition,

. Below that are the matrices of

,

, and

. The graphic shows how these matrices act on a cube centered at the origin, with faces orthogonal to the axes. The brightest cube is fixed, and displayed only as a point of reference. The middle cube (slightly darker) shows the action of

on the fixed cube, where the gray line shows the axis of rotation. The action of

is first, since the operation throughout is composition. The third and darkest cube shows both the action of

on the cube already acted on by

and the action of

on the fixed cube. The thinner gray line shows the axis of rotation of

and the thicker gray line shows the the axis of rotation of the composition

. By experimenting with different elements and compositions of elements, you can verify that

is isomorphic to the group of rotations of the cube.