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Hyperbolic spaceforms with ‘Schläfli solid’ (8, 8, 3). (English) Zbl 1274.57013

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).

MSC:

57S30 Discontinuous groups of transformations
51M10 Hyperbolic and elliptic geometries (general) and generalizations
51M20 Polyhedra and polytopes; regular figures, division of spaces
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