In geometry, orbifold notation (or orbifold signature) is a system, invented by the mathematician William Thurston and promoted by John Conway, for representing types of symmetry groups in two-dimensional spaces of constant curvature.
The following types of Euclidean transformation can occur in a group described by orbifold notation: All translations which occur are assumed to form a discrete subgroup of the group symmetries being described.
A string not written in boldface represents a group of symmetries of the Euclidean plane, which is assumed to contain two independent translations.
An object is chiral if its symmetry group contains no reflections; otherwise it is called achiral.
Indeed, Conway's "Magic Theorem" indicates that the 17 wallpaper groups are exactly those with the sum of the feature values equal to 2.
The bullet (•) is added on one- and two-dimensional groups to imply the existence of a fixed point.