This is an exercise in Allen Hatcher's Algebraic Topology book(page 53, 7)
Let X be the quotient space of $S^2$ obtained by identifying the north and south poles to a single point.Put a cell complex structure on X and use this to compute $\pi_1(X)$.
How to cut X to see how many 0-cells,1-cells and 2-cells.I use a way to cut X from up to down through the identified point,so each half is constructed by 3 0-cells,4 1-cells and 1 2-cell.Am I right?I'm a little suspicious.