The cubical complex of a permutation group representation - or however   you want to call it
  This paper is about a small combinatorial trick, which is well known, but has no name. Let G be a permutation group acting on a vector space M. There is a natural way to assign a cosimplicial space to these data. We call the resulting cochain complex the cubical complex. Its cohomology is easy to compute. We give some examples of its occurrence in nature. 
Pavol Severa and Thomas Willwacher
math.QA