Molnár, Emil; Prok, István Hyperbolic spaceforms with ‘Schläfli solid’ (8, 8, 3). (English) Zbl 1274.57013 Symmetry Cult. Sci. 22, No. 1-2, 247-261 (2011). Summary: We illustrate a typical but not easy method for constructing orientable compact 3-manifolds of hyperbolic metric, i.e. hyperbolic spaceforms. At he same time we get hyperbolic fundamental tilings under fixed-point-free isometry groups. By computer and via projective metrics, we determine the 3 non-homeomorphic (so non-isometric) hyperbolic spaceforms with hyperbolic “Archimedean solid” of Schläfli symbol (8, 8, 3). Cited in 2 Documents MSC: 57S30 Discontinuous groups of transformations 51M10 Hyperbolic and elliptic geometries (general) and generalizations 51M20 Polyhedra and polytopes; regular figures, division of spaces Keywords:hyperbolic spaceform; projective metrics; truncated cube of Schläfli symbol (8, 8, 3); polyhedral manifolds PDFBibTeX XMLCite \textit{E. Molnár} and \textit{I. Prok}, Symmetry Cult. Sci. 22, No. 1--2, 247--261 (2011; Zbl 1274.57013)