References
- [Akiyoshi 01] H. Akiyoshi. “Finiteness of Polyhedral Decompositions of Cusped Hyperbolic Manifolds obtained by the Epstein–Penner’s Method.” Proc. Amer. Math. Soc. 129:8 (2001), 2431–2439.
- [Beardon 95] A. F. Beardon. The geometry of discrete groups, volume 91 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1995. Corrected reprint of the 1983 original.
- [Billera et al. 90] L. J. Billera, P. Filliman, and B. Sturmfels. “Constructions and Complexity of Secondary Polytopes.” Adv. Math. 83:2 (1990), 155–179.
- [Billera and Sturmfels 92] L. J. Billera and B. Sturmfels. “Fiber Polytopes.” Ann. of Math. (2) 135:3 (1992), 527–549.
- [Cannon et al. 97] J. W. Cannon, W. J. Floyd, R. Kenyon, and W. R. Parry. Hyperbolic geometry. In Flavors of geometry, volume 31 of Math. Sci. Res. Inst. Publ., pp. 59–115. Cambridge Univ. Press, Cambridge, 1997.
- [Cooper and Long 15] D. Cooper and D. D. Long. “A Generalization of the Epstein–Penner Construction to Projective Manifolds.” Proc. Amer. Math. Soc. 143:10 (2015), 4561–4569.
- [De Loera et al. 10] J. A. De Loera, J. Rambau, and F. Santos. Triangulations, volume 25 of Algorithms and Computation in Mathematics. Berlin: Springer-Verlag, 2010.
- [Epstein and Penner 88] D. B. A. Epstein and R. C. Pen- ner. “Euclidean Decompositions of Noncompact Hyperbolic Manifolds.” J. Differential Geom. 27:1 (1988), 67–80.
- [Fillastre and Izmestiev 17] F. Fillastre and I. Izmestiev. “Shapes of Polyhedra, Mixed Volumes and Hyperbolic Geometry.” Mathematika 63:1 (2017), 124–183.
- [Gawrilow and Joswig 00] E. Gawrilow and M. Joswig. polymake: a framework for analyzing convex polytopes. In Gil Kalai and Gunter M. Ziegler, editors, Polytopes — Combinatorics and Computation, pp. 43–74. Birkhauser, 2000.
- [Gelfand et al. 08] I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinsky. Discriminants, Resultants and Multidimensional Determinants. Birkhäuser, Boston, 2008. Reprint of the 1994 edition.
- [Gu et al. 13] X. Gu, F. Luo, J. Sun, and T. Wu. A discrete uniformization theorem for polyhedral surfaces. arXiv:1309.4175v1 [math.GT], 2013.
- [Haiman 84] M. Haiman. Constructing the associahedron. Unpublished manuscript, 1984.
- [Jensen 17] A. N. Jensen. Gfan, a software system for Gröb- ner fans and tropical varieties, version 0.6. Available at http://home.imf.au.dk/jensen/software/gfan/gfan.html, 2017.
- [Kapovich 09] M. Kapovich. Hyperbolic manifolds and discrete groups. Modern Birkhäuser Classics. Birkhäuser Boston, Inc., Boston, MA, 2009. Reprint of the 2001 edition.
- [Katok 92] S. Katok. Fuchsian Groups. Chicago, IL: Chicago Lectures in Mathematics. University of Chicago Press, 1992.
- [Lee 89] C. W. Lee. “The Associahedron and Triangulations of the n-gon.” European J. Combin. 10:6 (1989), 551–560.
- [Lehner 66] J. Lehner. A short course in automorphic functions. New York: Holt, Rinehart and Winston, 1966.
- [McMullen 73] P. McMullen. “Representations of Polytopes and Polyhedral Sets.” Geometriae Dedicata 2 (1973), 83–99.
- [Penner 87] R. C. Penner. “The Decorated Teichmüller Space of Punctured Surfaces.” Commun. Math. Phys. 113:2 (1987), 299–339.
- [Penner 12] R. C. Penner. Decorated Teichmüller Theory. QGM Master Class Series. Zurich: European Mathematical Society, 2012.
- [Shephard 71] G. C. Shephard. “Spherical Complexes and Radial Projections of Polytopes.” Israel J. Math. 9 (1971), 257–262.
- [Springborn 17] B. Springborn. Hyperbolic polyhedra and discrete uniformization. arXiv:1707.06848 [math.MG], 2017.
- [Stasheff 63] J. D. Stasheff. “Homotopy Associativity of H- Spaces. I, II.” Trans. Amer. Math. Soc. 108 (1963), 275–292; ibid. 108 (1963), 293–312.
- [Thurston 97] W. P. Thurston. Three-dimensional geometry and topology. Vol. 1, volume 35 Princeton Mathematical Series. Princeton, NJ: Princeton University Press, 1997. Edited by Silvio Levy.
- [Tillmann and Wong 16] S. Tillmann and S. Wong. “An Algorithm for the Euclidean Cell Decomposition of a Cusped Strictly Convex Projective Surface.” J. Comput. Geom. 7:1 (2016), 237–255.
- [Weeks 93] J. R. Weeks. “Convex Hulls and Isometries of Cusped Hyperbolic 3-Manifolds.” Topology Appl. 52:2 (1993), 127–149.