  A crystallographic arrangement is a set of linear hyperplanes satisfying a
certain integrality property and decomposing the space into simplicial cones.
Crystallographic arrangements were completely classified in a series of papers
by Heckenberger and the author. However, this classification is based on two
computer proofs checking millions of cases. In the present paper, we prove
without using a computer that, up to equivalence, there are only finitely many
irreducible crystallographic arrangements in each rank greater than two.
