Boundary subcomplex of a simplex
= Boundary subcomplex of a simplex
{title2=$\partial\Delta^n$}
The boundary subcomplex $\partial\Delta^n$ consists of all proper faces of the $n$-simplex. Its <geometric realization of a simplicial complex> is homeomorphic to the <sphere> $S^{n-1}$, while $|\Delta^n|$ is homeomorphic to the <closed disk> $D^n$.