What is the proper symmetry group of a cube in which three faces where none are opposite each other are painted yellow and the other faces are blue?
Any idea on where to start
Thank you
What is the proper symmetry group of a cube in which three faces where none are opposite each other are painted yellow and the other faces are blue?
Any idea on where to start
Thank you
For me it is easier to think of blue tetrahedron and a yellow tetrahedron glued together along one face. The symmetry group then is just the symmetry group of the tetrahedron, with one face mapped to itself: there is rotation of period 3 (on an axis perpendicular to the fixed face), and a flip (about a plane perpendicular to the fixed face). The dihedral group of triangle.