Point Groups in Three Dimensions - Relation Between Orbifold Notation and Order

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:

    We must get back into relation, vivid and nourishing relation to the cosmos and the universe. The way is through daily ritual, and is an affair of the individual and the household, a ritual of dawn and noon and sunset, the ritual of the kindling fire and pouring water, the ritual of the first breath, and the last.
    —D.H. (David Herbert)

    All things being equal, I would choose a woman over a man in order to even the balance of power, to insinuate a different perspective into the process, to give young women something to shoot for and someone to look up to. But all things are rarely equal.
    Anna Quindlen (b. 1952)