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This paper is about a small combinatorial trick, which is well known, but hasno name. Let G be a permutation group acting on a vector space M. There is anatural way to assign a cosimplicial space to these data. We call the resultingcochain complex the cubical complex. Its cohomology is easy to compute. We givesome examples of its occurrence in nature.

The cubical complex of a permutation group representation - or however you want to call it