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)
“I’ve never been afraid to step out and to reach out and to move out in order to make things happen.”
—Victoria Gray, African American civil rights activist. As quoted in This Little Light of Mine, ch. 3, by Hay Mills (1993)