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.