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## The smallest hyperbolic 6-manifolds

### Brent Everitt, John Ratcliffe, and Steven Tschantz

**Abstract.**
By gluing together copies of an all right-angled Coxeter polytope
a number of open hyperbolic $6$-manifolds
with Euler characteristic $-1$ are constructed. They are the first known
examples of hyperbolic $6$-manifolds having the smallest possible volume.

*Copyright 2005 American Mathematical Society
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#### Article Info

- ERA Amer. Math. Soc.
**11** (2005), pp. 40-46
- Publisher Identifier: S 1079-6762(05)00145-9
- 2000
*Mathematics Subject Classification*. Primary 57M50
- Received by editors October 31, 2004
- Posted on May 27, 2005
- Communicated by Walter Neumann
- Comments (When Available)

**Brent Everitt**

Department of Mathematics, University of York, York YO10 5DD, England

*E-mail address:* `bje1@york.ac.uk`

**John Ratcliffe**

Department of Mathematics, Vanderbilt University, Nashville, TN 37240

*E-mail address:* `ratclifj@math.vanderbilt.edu`

**Steven Tschantz**

Department of Mathematics, Vanderbilt University, Nashville, TN 37240

*E-mail address:* `tschantz@math.vanderbilt.edu`

The first author is grateful to the Mathematics Department, Vanderbilt
University for its hospitality during a stay when the results of this paper
were obtained.

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