What is the CW-complex of Eilenberg-MacLane space $K(\mathbb{Z}_2,2)$?

What is the CW-complex of Eilenberg-MacLane space $K(\mathbb{Z}_n,d)$?

What is the CW-complex of Eilenberg-MacLane space $K(\mathbb{Z}_n\times \mathbb{Z}_m,d)$?

For example, I like to know the number of cells in each dimensions, and the chain complex formed by those cells, so that one can compute cohomology. (I like to know the chain complex, in addition to the cohomology).

theCW-complex". Take a CW-complex representing $K(\mathbb{Z}_n, d)$, cross it with $[0,1]$ -- boom, you've got a new one. $\endgroup$ – Najib Idrissi Feb 2 '18 at 16:23