Orbifold notation is a compact notation for two-dimensional discrete symmetry groups based on the quotient orbifold. Positive integers record
rotational cone points. Integers following an asterisk record corner reflectors on
mirror boundaries, while the symbols 
and 
record a handle and a crosscap, respectively. Omitting a feature
omits its symbol.
For example, the notation 
describes a reflection group whose fundamental region is
a triangle with corner orders 6, 3, and 2. The notation records the topology and
singular data of the quotient rather than a particular choice of generators.
