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:
“There is a constant in the average American imagination and taste, for which the past must be preserved and celebrated in full-scale authentic copy; a philosophy of immortality as duplication. It dominates the relation with the self, with the past, not infrequently with the present, always with History and, even, with the European tradition.”
—Umberto Eco (b. 1932)
“In order for the wheel to turn, for life to be lived, impurities are needed, and the impurities of impurities in the soil, too, as is known, if it is to be fertile. Dissension, diversity, the grain of salt and mustard are needed: Fascism does not want them, forbids them, and that’s why you’re not a Fascist; it wants everybody to be the same, and you are not. But immaculate virtue does not exist either, or if it exists it is detestable.”
—Primo Levi (1919–1987)