Abstract
Let σ(n) be the minimum number of ideal hyperbolic tetrahedra necessary to construct a finite volumen-cusped hyperbolic 3-manifold, orientable or not. Let σor(n) be the corresponding number when we restrict ourselves to orientable manifolds. The correct values of σ(n) and σor(n) and the corresponding manifolds are given forn=1,2,3,4 and 5. We then show that 2n−1≤σ(n)≤σor(n)≤4n−4 forn≥5 and that σor(n)≥2n for alln.
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Both authors were supported by NSF Grants DMS-8711495, DMS-8802266 and Williams College Research Funds.
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Adams, C., Sherman, W. Minimum ideal triangulations of hyperbolic 3-manifolds. Discrete Comput Geom 6, 135–153 (1991). https://doi.org/10.1007/BF02574680
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DOI: https://doi.org/10.1007/BF02574680