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 not to envy the man who can dismiss reason, although we know how it must turn out at last.”
—Charles Sanders Peirce (1839–1914)
“One can describe a landscape in many different words and sentences, but one would not normally cut up a picture of a landscape and rearrange it in different patterns in order to describe it in different ways. Because a photograph is not composed of discrete units strung out in a linear row of meaningful pieces, we do not understand it by looking at one element after another in a set sequence. The photograph is understood in one act of seeing; it is perceived in a gestalt.”
—Joshua Meyrowitz, U.S. educator, media critic. “The Blurring of Public and Private Behaviors,” No Sense of Place: The Impact of Electronic Media on Social Behavior, Oxford University Press (1985)