For n=1. We consider two copies of $\Delta^1$, $1$ simplicies and identifying their boundaries we get a loop, that is $S^1$.
For n=2, identifying boundaries of two copies of $\Delta^2$ via identify map, we get a compact convex subset of $R^3$, hence it is $S^2$.
These give $\Delta$ complex structure of $S^1$ and $S^2$.
How do we visualize this standard $\Delta$ complex structure for $S^n$ in general?