Geometrically, the space V on which S ~ ~ 2 acts is a line, with infinitely many equally spaced reflections. It is natural to identify the line V with the real line R 1 , s 0 with reflection around the point 0, and s 1 with reflection around the point 1. In this case, the reflection ( s 0 s 1 ) k s 0 reflects across the point – k for any integer k, the composition s 0 s 1 translates the line by –2, and the composition s 1 s 0 translates the line by 2.