Minimum ideal triangulations of hyperbolic 3-manifolds

@article{Adams1991MinimumIT,
title={Minimum ideal triangulations of hyperbolic 3-manifolds},
journal={Discrete \& Computational Geometry},
year={1991},
volume={6},
pages={135-153}
}
• Published 1 March 1991
• Mathematics
• Discrete & Computational Geometry
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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