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pages 323-347
Unravelling the Dodecahedral Spaces
Publication type: Book Chapter
Publication date: 2018-04-10
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).
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TY - GENERIC
DO - 10.1007/978-3-319-72299-3_17
UR - https://doi.org/10.1007/978-3-319-72299-3_17
TI - Unravelling the Dodecahedral Spaces
T2 - MATRIX Book Series
AU - Spreer, Jonathan
AU - Tillmann, Stephan
PY - 2018
DA - 2018/04/10
PB - Springer Nature
SP - 323-347
SN - 2523-3041
SN - 2523-305X
ER -
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@incollection{2018_Spreer,
author = {Jonathan Spreer and Stephan Tillmann},
title = {Unravelling the Dodecahedral Spaces},
publisher = {Springer Nature},
year = {2018},
pages = {323--347},
month = {apr}
}