Square quotient model of the two-sphere
= Square quotient model of the two-sphere
Identify the vertical sides of $[0,1]^2$, then collapse each horizontal side separately to a point. The resulting quotient is homeomorphic to $S^2$ through
$$
(x,y)\longmapsto
\bigl(\sin(\pi y)\cos(2\pi x),
\sin(\pi y)\sin(2\pi x),\cos(\pi y)\bigr).
$$
Equivalently, the quotient is the suspension of the circle.