While studying group (co)-homology, I've learned about how to construct a chain complex such that its cell chain complex coïnide with the bar resolution of a certain group $G$. For that we first construct the space $EG$ such that its $0$-cells are $G$, its $1$-cells are given by $G\times G$ such that each pair $(g,h)$ are glued to the $0$-skeleton by identifying its end points with the $0$-cells h and g. And in general we add $G^{n+1}$ n-cells each homeomorphic to the standard simplices $\Delta ^n$, for each $(g_0,...,g_n)=\sigma$ we have an n-cell $\Delta^{\sigma}=\Delta^n$ and we identify its faces $\delta_i\Delta^{\sigma}$ with $\Delta^{\delta_i \sigma}$.
So my problem is that I have a hard time to visualize what this first space $EG$ would look like. I've tried to compute it for a simple group like $C_2$ but without much success, maybe someone has a visual example that could help me to understand this first step of the construction ?