  A cohomology theory is proposed for the recently discovered heptagon relation
-- an algebraic imitation of a 5-dimensional Pachner move 4--3. In particular,
`quadratic cohomology' is introduced, and it is shown that it is quite
nontrivial, and even more so if compare heptagon with either its higher
analogues, such as enneagon or hendecagon, or its lower analogue, pentagon.
Explicit expressions for the nontrivial quadratic heptagon cocycles are found
in dimensions 4 and 5.
