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Conformal Geometry and Dynamics
Conformal Geometry and Dynamics
ISSN 1088-4173


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 | References | Similar Articles | Additional Information

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.

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Additional Information

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

PII: S 1088-4173(98)00025-3
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

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