Relation Between Orbifold Notation and Order
The order of each group is 2 divided by the orbifold Euler characteristic; the latter is 2 minus the sum of the feature values, assigned as follows:
- n without or before * counts as (n−1)/n
- n after * counts as (n−1)/(2n)
- * and x count as 1
This can also be applied for wallpaper groups and frieze groups: for them, the sum of the feature values is 2, giving an infinite order; see orbifold Euler characteristic for wallpaper groups
Read more about this topic: Point Groups In Three Dimensions
Famous quotes containing the words relation and/or order:
“Light is meaningful only in relation to darkness, and truth presupposes error. It is these mingled opposites which people our life, which make it pungent, intoxicating. We only exist in terms of this conflict, in the zone where black and white clash.”
—Louis Aragon (1897–1982)
“It’s not greed and ambition that makes wars—it’s goodness. Wars are always fought for the best of reasons, for liberation or manifest destiny, always against tyranny and always in the best interests of humanity. So far this war, we’ve managed to butcher some 10,000,000 people in the interest of humanity. The next war, it seems we’ll have to destroy all of man in order to preserve his damn dignity.”
—Paddy Chayefsky (1923–1981)