Tilings in Hyperbolic Space in an Arbitrary Dimension

Of a special interest are tilings in hyperbolic n–space. The present work studies tilings in hyperbolic n–space of arbitrary dimension by polytopes. The best behaved tilings are the face-to-face tilings by convex polytopes. The main results of this publication are obtained for tilings (isohedral, non-isohedral, face-to-face, non- face-to- face) in the hyperbolic n–space of arbitrary dimension for any n, (n ≥ 2) by compact and non-compact polytopes and we describe their discrete isometry groups and properties. Torsion free groups are especially important.