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

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