Unravelling the Dodecahedral Spaces
arXiv:1702.08080 · doi:10.1007/978-3-319-72299-3_17
Abstract
The hyperbolic dodecahedral space of Weber and Seifert has a natural non-positively curved cubulation obtained by subdividing the dodecahedron into cubes. We show that the hyperbolic dodecahedral space has a 6-sheeted irregular cover with the property that the canonical hypersurfaces made up of the mid-cubes give a very short hierarchy. Moreover, we describe a 60-sheeted cover in which the associated cubulation is special. We also describe the natural cubulation and covers of the spherical dodecahedral space (aka Poincaré homology sphere).
15 pages + 6 pages appendix, 7 figures, 4 tables