caa a22 4500 388046686 CHVBK 20180307125040.0 cr unu---uuuuu 161130e199802 xx s 000 0 eng 10.1017/S1446788700001294 doi S1446788700001294 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700001294 Marshall T. H. Department of Mathematics University of Auckland Private Bag 92019 Auckland New Zealand Truncated tetrahedra and their reflection groups [Elektronische Daten] [T. H. Marshall] We outline the classification, up to isometry, of all tetrahedra in hyperbolic space with one or more vertices truncated, for which the dihedral angles along the edges formed by the truncations are all π/2, and those remaining are all submultiples of π. We show how to find the volumes of these polyhedra, and find presentations and small generating sets for the orientation-preserving subgroups of their reflection groups. For particular families of these groups, we find low index torsion free subgroups, and construct associated manifolds and manifolds with boundary. In particular, for each g ≥ 2, we find a sequence of hyperbolic manifolds with totally geodesic boundary of genus g, which we conjecture to be of least volume among such manifolds. Copyright © Australian Mathematical Society 1998 primary 30F40 nationallicence 57N10 nationallicence secondary 20F55 nationallicence Coxeter polytope nationallicence truncated tetrahedron nationallicence co-volume nationallicence torsion-free subgroup nationallicence hyperbolic manifold nationallicence Journal of the Australian Mathematical Society Cambridge University Press 64/1(1998-02), 54-72 1446-7887 64:1<54 1998 64 JAZ https://doi.org/10.1017/S1446788700001294 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700001294 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Marshall T. H. Department of Mathematics University of Auckland Private Bag 92019 Auckland New Zealand NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 64/1(1998-02), 54-72 1446-7887 64:1<54 1998 64 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge