Let $S_k$ be  the set of all permutations of $k+1$ elements $0,1,...,k$. introduce boundary maps $d_i : S_k \rightarrow  S_{k-1}$ by deleting from permutation $\eta$ element $\eta(i)$ and monotone reordering and degeneracy  
$s_i :S_k \rightarrow S_{k+1} $ by inserting into permutation $\eta$ a new element $\eta(i)+1/2$ right after $\eta(i)$ and monotone reordering. It is a simplicial set, contractible and classifies reorderings of simplicial sets. 

Is it known? May be in higher symmetric something?