PhDorBust
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I'm having trouble visualizing some of the rotations that compose this group.
Clearly the group has 24 elements by argument any of 6 faces can be up, and then cube can assume 4 different positions for each upwards face.
My book describes the rotations as follows:
3 subgroups of order 4 created by rotation about line passing through center of two faces.
4 subgroups of order 3 created by "taking hold of a pair of diagonally opposite vertices and rotating through the three possible positions, corresponding to the three edges emanating from each vertex."
My trouble lies with the second description, that is, I haven't the slightest idea of what it is saying. Any help? Also, any general comments on visualizing symmetry groups would be appreciated, I trouble going beyond dihedral group of order 4.
Clearly the group has 24 elements by argument any of 6 faces can be up, and then cube can assume 4 different positions for each upwards face.
My book describes the rotations as follows:
3 subgroups of order 4 created by rotation about line passing through center of two faces.
4 subgroups of order 3 created by "taking hold of a pair of diagonally opposite vertices and rotating through the three possible positions, corresponding to the three edges emanating from each vertex."
My trouble lies with the second description, that is, I haven't the slightest idea of what it is saying. Any help? Also, any general comments on visualizing symmetry groups would be appreciated, I trouble going beyond dihedral group of order 4.
