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 adding 1 to all elements with $\eta(j)>\eta(i)$  and incerting into the result a new element $\eta(i)+1$ right after $\eta(i)$ on $i+1$ place. It is a simplicial set, contractible and classifies reorderings of simplicial sets. 

Is it known? May be in higher symmetric something?

(Update) Boris Tsygan pointed the right direction in [Facebook duscussion][1]


  [1]: https://m.facebook.com/story.php?story_fbid=10157493966588914&id=811018913