An inequality for polyhedra and ideal triangulations of cusped hyperbolic 3-manifolds

Wada, Masaaki; Yamashita, Yasushi; Yoshida, Han

doi:10.1090/S0002-9939-96-03563-0

An inequality for polyhedra and ideal triangulations of cusped hyperbolic 3-manifolds
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by Masaaki Wada, Yasushi Yamashita and Han Yoshida PDF

Proc. Amer. Math. Soc. 124 (1996), 3905-3911 Request permission

Abstract:

It is not known whether every noncompact hyperbolic 3-manifold of finite volume admits a decomposition into ideal tetrahedra. We give a partial solution to this problem: Let $M$ be a hyperbolic 3-manifold obtained by identifying the faces of $n$ convex ideal polyhedra $P_{1},\dots ,P_{n}$. If the faces of $P_{1},\dots ,P_{n-1}$ are glued to $P_{n}$, then $M$ can be decomposed into ideal tetrahedra by subdividing the $P_{i}$’s.

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