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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A hyperbolic $ 4$-manifold


Author: Michael W. Davis
Journal: Proc. Amer. Math. Soc. 93 (1985), 325-328
MSC: Primary 57N13; Secondary 51M10, 52A25
MathSciNet review: 770546
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Abstract: There is a regular $ 4$-dimensional polyhedron with 120 dodecahedra as $ 3$-dimensional faces. (Coxeter calls it the "$ 120$-cell".) The group of symmetries of this polyhedron is the Coxeter group with diagram:

$\displaystyle [unk]$

For each pair of opposite $ 3$-dimensional faces of this polyhedron there is a unique reflection in its symmetry group which interchanges them. The result of identifying opposite faces by these reflections is a hyperbolic manifold $ {M^4}$.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0770546-7
PII: S 0002-9939(1985)0770546-7
Article copyright: © Copyright 1985 American Mathematical Society