Advanced search
Publication Cover
Experimental Mathematics Volume 17, 2008 - Issue 4
Submit an article Journal homepage
23
Views
2
CrossRef citations to date
0
Altmetric
Original Article

The 191 Orientable Octahedral Manifolds

Damian Heard RedTribe, Carlton, Victoria, Australia 3053
,
Ekaterina Pervova Dipartimento di Matematica Applicata, Via Filippo Buonarroti, 1C, 56127 Pisa, Italy
&
Carlo Petronio Dipartimento di Matematica Applicata, Via Filippo Buonarroti, 1C, 56127 Pisa, Italy
Pages 473-486 | Published online: 30 Jan 2011

  • R. Benedetti and C. Petronio. Lectures on Hyperbolic Geometry. New York: Springer-Verlag, 1992.
  • P. J. Callahan, M. V. Hildebrandt, and J. R. Weeks. "A Census of Cusped Hyperbolic 3-Manifolds," with microfiche supplement. Math. Comp. 68 (1999), 321-332.
  • D. Coulson, O. Goodman, C. Hodgson, and W. Neumann. "Computing Arithmetic Invariants of 3-Manifolds." Experiment. Math. 9 (2000), 127-152.
  • D. B. A. Epstein and R. C. Penner. "Euclidean Decomposition of Non-compact Hyperbolic Manifolds." J. Differential Geom. (1) 27 (1988), 67-80.
  • A. T. Fomenko and S. V. Matveev. Algorithmic and Computer Methods for Three-Manifolds, Mathematics and Its Applications 425. Dordrecht: Kluwer Academic Publishers, 1997.
  • R. Frigerio and C. Petronio. "Construction and Recognition of Hyperbolic 3-Manifolds with Geodesic Boundary." Trans. Amer. Math. Soc. 356 (2004), 3243-3282.
  • R. Frigerio, B. Martelli, and C. Petronio. "Small Hyperbolic 3-Manifolds with Geodesic Bboundary." Experiment. Math. 13 (2004), 171-184.
  • R. Frigerio, B. Martelli, and C. Petronio. "Hyperbolic 3-Manifolds with Non-empty Boundary." Tables available online (www.dm.unipi.it/pages/petronio/ public_html).
  • O. Goodman. "Snap," A Computer Program for Studying Arithmetic Invariants of Hyperbolic 3-Manifolds. Available online (http://www.ms.unimelb.edu.au/εsnap/).
  • W. Haken. "Theorie der Normalflachen: Ein Isotopiekriterium für den Kreisknoten." Acta Math. 105 (1961), 245-375.
  • D. Heard. "Orb," A Computer Program for Finding Hyperbolic Structures on Hyperbolic 3-Orbifolds and 3-Manifolds. Available online ( http://www.ms.unimelb.edu. au/εsnap/orb.html
  • Damian Heard, Ekaterina Pervova, and Carlo Petronio. "Census of the 191 Orientable Octahedral Manifolds." Available online ( http://www.dm.unipi. it/pages/petronio/public_html/octa.html
  • J. Hempel. 3-Manifolds, Ann. of Math. Studies 86. Princeton: Princeton University Press, 1976.
  • W. Jaco and P. B. Shalen. "A New Decomposition Theorem for Irreducible Sufficiently-Large 3-Manifolds." Algebraic and Geometric Topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976), part 2, pp. 71-84, Proc. Sympos. Pure Math. XXXII. Providence: Amer. Math. Soc., 1978.
  • K. Johannson. Homotopy Equivalences of 3-Manifolds with Boundaries, Lecture Notes in Mathematics 761. Berlin: Springer-Verlag, 1979.
  • S. Kojima. "Polyhedral Decomposition of Hyperbolic Manifolds with Boundary." Proc. Work. Pure Math. 10 (1990), 37-57.
  • S. Kojima. "Polyhedral Decomposition of Hyperbolic 3-Manifolds with Totally Geodesic Boundary." In Aspects of Low-Dimensional Manifolds, pp. 93-112, Adv. Stud. Pure Math. 20. Tokyo: Kinokuniya, 1992.
  • S. V. Matveev. Algorithmic Topology and Classification of 3-Manifolds, ACM Monographs 9. New York: Springer, 2003.
  • S. V. Matveev and V. V. Tarkaev, "Three-manifold Recognizer," A Computer Program for Recognition of 3-Manifolds. Available online ( http://www.csu.ac.ru/εtrk/spine/
  • G. Perelman. "The Entropy Formula for the Ricci Flow and Its Geometric Applications." Preprint; math.DG/0211159, 2002.
  • G. Perelman. "Ricci Flow with Surgery on Three-Manifolds." Preprint; math.DG/0303109, 2003.
  • G. Perelman. "Finite Extinction Time for the Solutions to the Ricci Flow on Certain Three-Manifolds." Preprint; math.DG/0307245, 2003.
  • J. G. Ratcliffe. Foundations of Hyperbolic Manifolds, 2nd edition, Graduate Texts in Math. 149. New York: Springer, 2006.
  • C. P. Rourke and B. J. Sanderson. Introduction to Piecewise-Linear Topology, Ergebn. der Math. 69. New York: Springer-Verlag, 1972.
  • M. Sakuma and J. R. Weeks. "The Generalized Tilt Formula." Geom. Dedicata 50 (1995), 1-9.
  • W. P. Thurston. "The Geometry and Topology of 3-manifolds." Mimeographed notes, Princeton, 1979.
  • V. G. Turaev and O. Ya. Viro. "State Sum Invariants of 3-Manifolds and Quantum 6j-Symbols." Topology (4) 31 (1992), 865-902.
  • A. Ushijima. "The Tilt Formula for Generalized Simplices in Hyperbolic Space." Discrete Comput. Geom. 28 (2002), 19-27.
  • A. Ushijima. "A Volume Formula for Generalised Hyperbolic Tetrahedra." In Non-Euclidean Geometries, pp. 249-265, Mathematics and Its Applications 581. New York: Springer, 2006.
  • J. R. Weeks. "SnapPea," The Hyperbolic Structures Computer Program. Available online ( http://www.geometrygames.org

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.