SO(3) as real projective three-space
= SO(3) as real projective three-space
{c}
{title2=$SO(3)\cong\mathbb{RP}^3$}
= SO(3) group manifold
{c}
{synonym}
The <Adjoint double cover from SU(2) to SO(3)> has kernel $\{I,-I\}$. Under <SU(2) as the three-sphere>, multiplication by $-I$ is the antipodal map, so the quotient is <Real projective space> $\mathbb{RP}^3$. Equivalently, an axis-angle ball of radius $\pi$ has opposite boundary points identified. The <fundamental group> is $\mathbb Z_2$.