Let G^+ be a finite subgroup of SO(3) acting on the sphere S^2 and F = {x | g G{e} : gx = x} be the set of all the points fixed by non-trivial elements of G^+ . Let A \subset F be a set containing exactly one point from each orbit of G^+ acting on F.

Prove the following:

- F is invariant under G^+

- |F| = |G^+| |A| - 2 ( |G^+| - 1)

Let G+ be a finite subgroup of SO(3) acting on the sphere S2 and F = {x | 39 G+ \{e} : gx = x} be the set of all the points fixed by non-trivial elements of G+. Let A C F be a set containing exactly one point from each orbit of G+ acting on F. Prove the following: . F is invariant under G+. [F] = {G+||A| 2(1G+| 1). Let G+ be a finite subgroup of SO(3) acting on the sphere S2 and F = {x | 39 G+ \{e} : gx = x} be the set of all the points fixed by non-trivial elements of G+. Let A C F be a set containing exactly one point from each orbit of G+ acting on F. Prove the following: . F is invariant under G+. [F] = {G+||A| 2(1G+| 1)