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Experimental Mathematics Volume 31, 2022 - Issue 1
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Original Articles

Exploring the List of Smallest Right-Angled Hyperbolic Polyhedra

Taiyo InoueDepartment of Sciences and Mathematics, California Maritime Academy, Vallejo, CA, USACorrespondence[email protected]
Pages 165-183 | Published online: 11 Apr 2019

References

  • [Agol et al. 07] I. Agol, N. M. Dunfield, P. A. Storm, and W. P. Thurston. “Lower Bounds on Volumes of Hyperbolic Haken 3-Manifolds.” J. Amer. Math. Soc. 20 (2007), 1053–1077.
  • [Andreev 70] E. M. Andreev. “Convex Polyhedra in Lobačevskiĭ Spaces.” Mat. Sb. (N.S.) 81:123 (1970), 445–478.
  • [Atkinson 09] C. K. Atkinson. “Volume Estimates for Equiangular Hyperbolic Coxeter Polyhedra.” Algeb. Geom. Topol. 9:2 (2009), 1225–1254.
  • [Gunn and Maxwell 91] C. Gunn and D. Maxwell. “Not Knot.” A. K. Peters, (1991). Video.
  • [Heard 13] D. Heard. “Orb. A Computer Program for Creating and Studying 3-Orbifolds.” http://www.ms.unimelb.edu.au/∼snap/orb.html, 2013.
  • [Inoue 08] T. Inoue. “Organizing Volumes of Right-Angled Hyperbolic Polyhedra.” Algebr. Geom. Topol. 8 (2008), 1523–1565.
  • [Löbell 31] F. Löbell. “Beispiele geschlossener dreidimensionaler Clifford-Kleinscher Räume negativer Krümmung.” Ber. Verh. Sächs. Akad. Leipzig 83 (1931), 167–174.
  • [Peixoto 15] T. Peixoto. “Graph-Tool A Python Module for Manipulation of Graphs.” https://graph-tool.skewed.de/, 2015.
  • [Pogorelov 67] A. V. Pogorelov. “Regular Decompostion of the Lobačevskiĭ Space.” Mat. Zametki 1 (1967), 3–8 (Russian).
  • [Rivin and Hodgson 93] I. Rivin and C. D. Hodgson. “A Characterization of Compact Convex Polyhedra In Hyperbolic 3-Space.” Invent. Math. 111:1 (1993), 77–111.
  • [Roeder et al. 07] R. K. W. Roeder, J. H. Hubbard, and W. D. Dunbar. “Andreev’s Theorem on Hyperbolic Polyhedra.” Ann. l’Institut Fourier 57:3 (2007), 825–882.
  • [Roeder 06] R. Roeder. “Hyper-hedron A Collection of Matlab Scripts for Constructing Hyperbolic Polyhedra.” https://www.math.iupui.edu/∼roederr/HYPER-HEDRON/, 2006.
  • [Vesnin 88] A. Vesnin. “Three-Dimensional Hyperbolic Manifolds of Löbell Type”. Sib. Math. J. 28:06 (1988), 731–734.
  • [Vesnin 17] A. Yu. Vesnin. “Right-Angled Polyhedra and Hyperbolic 3-Manifolds.” Russian Mathematical Surveys, 72:2 (2017), 335.
  • [Vesnin and Repovsh 11] A. Yu. Vesnin and D. Repovsh. “Two-Sided Bounds for the Volumes of Right-Angled Hyperbolic Polyhedra.” Mat. Zamet. 89:1 (2011), 12–18.
  • [Weeks 01] J. Weeks. “SnapPea: A Computer Program for Creating and Studying Hyperbolic 3-Manifolds.” 2001.

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