Symmetry of the cube
If we want to visualize the effect of the various tranformation on a cube, it could be useful to consider an object inside a cube and observe the effect of a transformation on it. For example, let's take a pyramid with a vertex in the centre of the cube, one vertex coinciding with a vertex of the cube, one vertex in the midpoint of a edge that is adjacent to the latter vertex and one vertex in the centre of a face that lays on this edge. In the figure we see that the effect of the composition of a rotation of 180° around a line t (that sends the light blue pyramid in the yellow pyramid) and of a rotation of 180° around a line s (that sends the yellow pyramid in the blue one) is equivalent to the effect of a rotation of 90° around the line r (that sends the light blue pyramid into the blue one).
The image has been used in the cards of the exhibition Simmetria, giochi di specchi.
© matematita
The image belongs to the sections...:
Symmetry of the cube (3D geometry)
