On a certain invariant of a finite unitary reflection group (Q923131)

Let V be a complex vector space of dimension m, G a finite reflection group, A the arrangement defined by G, i.e. the set of reflecting hyperplanes of elements in G. For some H in A, let \(A''\) be the set \(\{\) \(H\cap K\}\), where \(K\in A\) and \(K\neq H\). Let n and \(n''\) denote the cardinalities of A and \(A''\), respectively. The author shows, if G is an irreducible unitary reflection group, then \(2n/m=n-n''+1\). He does not use the classification of irreducible unitary reflection groups in his proof.