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Conformal Geometry and Dynamics

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Volume formulae for regular hyperbolic cubes

Author: T. H. Marshall
Journal: Conform. Geom. Dyn. 2 (1998), 25-28
MSC (1991): Primary 51M10, 51M25, 52A35, 52A38; Secondary 05B45, 51M20, 52A40
Published electronically: February 11, 1998
MathSciNet review: 1600384
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Abstract: We express the volume of a regular cube in hyperbolic $n$-space as an integral on $[0, \infty)$, and derive from this an asymptotic volume formula for the regular ideal hyperbolic $n$-cube. This in turn is applied to finding an asymptotic lower bound for the least number of simplices into which a Euclidean $n$-cube can be triangulated.

References [Enhancements On Off] (What's this?)

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  • 2. Uffe Haagerup and Hans J. Munkholm, Simplices of maximal volume in hyperbolic 𝑛-space, Acta Math. 147 (1981), no. 1-2, 1–11. MR 631085, 10.1007/BF02392865
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Additional Information

T. H. Marshall
Affiliation: Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand

Keywords: Hyperbolic cube, volume, simplex, triangulation
Received by editor(s): August 15, 1997
Received by editor(s) in revised form: November 26, 1997
Published electronically: February 11, 1998
Article copyright: © Copyright 1998 American Mathematical Society