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Journal Article

# A Hyperbolic 4-Manifold

Michael W. Davis
Proceedings of the American Mathematical Society
Vol. 93, No. 2 (Feb., 1985), pp. 325-328
DOI: 10.2307/2044771
Stable URL: http://www.jstor.org/stable/2044771
Page Count: 4

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Topics: Tessellations, Polyhedrons, Hyperplanes, Vertices, Isotropy
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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: $\cdot \underline 5 \cdot \underline \cdot \underline \cdot$ 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 M4.

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