Symmetry of the cube
The antipodal transformation is an element of the symmetry group of the cube. Here we can see the effct of the transfomation on the 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. The antipodal transformation sends the light blue pyramid in the violet one and the same effect is obtained by composing a reflection on the plane P (that sends the light blue pyramid in the red one) with a rotation of 180° around a line s perpendicular to P (that sends the red pyramid in the violet one).
The image has been used in the cards of the exhibition Simmetria, giochi di specchi - Symmetry, playing with mirrors.
© matematita
The image belongs to the sections...:
Symmetry of the cube (3D geometry)
