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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- T. H. Marshall
- Affiliation: Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
- Email: email@example.com
- Received by editor(s): August 15, 1997
- Received by editor(s) in revised form: November 26, 1997
- Published electronically: February 11, 1998
- © Copyright 1998 American Mathematical Society
- Journal: Conform. Geom. Dyn. 2 (1998), 25-28
- MSC (1991): Primary 51M10, 51M25, 52A35, 52A38; Secondary 05B45, 51M20, 52A40
- DOI: https://doi.org/10.1090/S1088-4173-98-00025-3
- MathSciNet review: 1600384