Let $\displaystyle X$ be the topological space obtained as the quotient of the sphere $\displaystyle S^2$ under the equivalence relation $\displaystyle x \sim -x$ for $\displaystyle x$ in the equatorial circle.

Describe a CW complex whose underlying space is $\displaystyle X$, and compute $\displaystyle H(X)$.

I know how to compute simplicial homology, I just can't describe the space in an adequate way, can anyone help me?