Impossible Discrete Symmetries
Since the overview is exhaustive, it also shows implicitly what is not possible as discrete symmetry group. For example:
- a C6 axis in one direction and a C3 in another
- a C5 axis in one direction and a C4 in another
- a C3 axis in one direction and another C3 axis in a perpendicular direction
etc.
Read more about this topic: Point Groups In Three Dimensions
Famous quotes containing the words impossible and/or discrete:
“It is impossible for a stranger traveling through the United States to tell from the appearance of the people or the country whether he is in Toledo, Ohio, or Portland, Oregon. Ninety million Americans cut their hair in the same way, eat each morning exactly the same breakfast, tie up the small girls’ curls with precisely the same kind of ribbon fashioned into bows exactly alike; and in every way all try to look and act as much like all the others as they can.”
—Alfred Harmsworth, Lord Northcliffe (1865–1922)
“The mastery of one’s phonemes may be compared to the violinist’s mastery of fingering. The violin string lends itself to a continuous gradation of tones, but the musician learns the discrete intervals at which to stop the string in order to play the conventional notes. We sound our phonemes like poor violinists, approximating each time to a fancied norm, and we receive our neighbor’s renderings indulgently, mentally rectifying the more glaring inaccuracies.”
—W.V. Quine (b. 1908)