# From angled triangulations to hyperbolic structures

```@article{Futer2010FromAT,
title={From angled triangulations to hyperbolic structures},
author={David Futer and Franccois Gu'eritaud},
journal={arXiv: Geometric Topology},
year={2010}
}```
• Published 3 April 2010
• Mathematics
• arXiv: Geometric Topology
This survey paper contains an elementary exposition of Casson and Rivin's technique for finding the hyperbolic metric on a 3-manifold M with toroidal boundary. We also survey a number of applications of this technique. The method involves subdividing M into ideal tetrahedra and solving a system of gluing equations to find hyperbolic shapes for the tetrahedra. The gluing equations decompose into a linear and non-linear part. The solutions to the linear equations form a convex polytope A. The…
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