Abstract
CONTENTS Introduction Chapter I. Acute-angled polytopes in Lobachevskii spaces § 1. The Gram matrix of a convex polytope § 2. The existence theorem for an acute-angled polytope with given Gram matrix § 3. Determination of the combinatorial structure of an acute-angled polytope from its Gram matrix § 4. Criteria for an acute-angled polytope to be bounded and to have finite volume Chapter II. Crystallographic reflection groups in Lobachevskii spaces § 5. The language of Coxeter schemes. Construction of crystallographic reflection groups § 6. The non-existence of discrete reflection groups with bounded fundamental polytope in higher-dimensional Lobachevskii spaces References