A flag in a simplical complex K in $\mathbb{R}^d$ is a nested sequence of proper faces, $\sigma_0 < \sigma_1 < ... < \sigma_k$. The collection of flags forms an abstract simplical complex A sometimes referred to as the order complex of K. Prove that A has a geometric realization in $\mathbb{R}^d$.
I guess what is confusing me the most is how to deal with the fact that the proper faces are nested.