Remark 1.2.3.12. The proof of Proposition 1.2.3.4 shows that the geometric realization $| S |$ of a simplicial set $S$ has a canonical realization as a CW complex, having one cell of dimension $n$ for each nondegenerate $n$-simplex $\sigma $ of $S$; this cell can be described explicitly as the image of the map
\[ | \Delta ^{n} | \setminus | \operatorname{\partial \Delta }^{n} | \hookrightarrow | \Delta ^{n} | \xrightarrow { \sigma } | S |. \]