= Real projective plane
{title2=$RP^2$}
{title2=$\projectiveSpace(\R^3)$}
{wiki}
For some reason, <Ciro Santilli> is mildly obsessed with understanding and visualizing the real projective plane.
To see why this is called a plane, move he center of the sphere to $z=1$, and project each line passing on the center of the sphere on the x-y plane. This works for all points of the sphere, except those at the equator $z=1$. Those are the <points at infinity>. Note that there is one such point at infinity for each direction in the x-y plane.