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 between, relation and/or order:
“We shall never resolve the enigma of the relation between the negative foundations of greatness and that greatness itself.”
—Jean Baudrillard (b. 1929)
“There is a certain standard of grace and beauty which consists in a certain relation between our nature, such as it is, weak or strong, and the thing which pleases us. Whatever is formed according to this standard pleases us, be it house, song, discourse, verse, prose, woman, birds, rivers, trees, room, dress, and so on. Whatever is not made according to this standard displeases those who have good taste.”
—Blaise Pascal (1623–1662)
“Yet whatever gains I had, these I have come to regard as loss because of Christ. More than that, I regard everything as loss because of the surpassing value of knowing Christ Jesus my Lord. For his sake I have suffered the loss of all things, and I regard them as rubbish, in order that I may gain Christ and be found in him, not having a righteousness of my own that comes from the law, but one that comes through faith in Christ, the righteousness from God based on faith.”
—Bible: New Testament, Philippians 3:7-9.