## SnapPea

 swMATH ID: 6873 Software Authors: Callahan, Patrick J.; Hildebrand, Martin V.; Weeks, Jeffrey R. Description: A program for creating and studying hyperbolic 3-manifolds. Each noncompact (or cusped) hyperbolic 3-manifold of finite volume can be decomposed into a finite collection of ideal hyperbolic tetrahedra. In the present work, a census is given for all hyperbolic 3-manifolds which can be obtained by gluing the faces of at most seven ideal tetrahedra. There are 6075 such manifolds, 4815 of them are orientable. The 103 manifolds obained from four or fewer tetrahedra are listed in an appendix to the paper, the others are in tables included on a microfiche supplement. In analogy with the enumeration of knots and links, each manifold is given a name indicating the number of ideal tetrahedra, the number of orientable and non-orientable cusps and finally its position in terms of increasing volume. For each manifold the following data are listed: volume, Chern-Simons invariant (if orientable), homology, symmetry or isometry group, shortest geodesic, chirality and a string of letters (code) from which the gluing pattern can be reconstructed. A description is given of how the enumeration has been carried out. As combinatorially there are too many gluing patterns already for a small number of tetrahedra, in a first step one has to find effective ways of eliminating a large number of gluings which could not possibly yield hyperbolic manifolds. Then in a second step computer programs as SnapPea are used to determine which of the remaining gluings in fact admit hyperbolic structures, to remove duplicates from the lists and to compute the various invariants. It is a hope that the lists may give hints on the distribution and on possible classification schemes for hyperbolic 3-manifolds, besides giving examples of small hyperbolic 3-manifolds with certain specific properties. Homepage: https://en.wikipedia.org/wiki/SnapPea Programming Languages: C Operating Systems: Mac OS X, Linux, and Windows Related Software: Snap; SnapPy; Regina; Magma; GAP; Knotscape; Orb; hikmot; SageMath; Trains; KnotInfo; PARI/GP; bfh_python; GitHub; Knot Atlas; Minksum; VisPak; Trelis; GeoCalcLib; VaryLab Cited in: 164 Publications
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### Cited by 191 Authors

 11 Petronio, Carlo 9 Dunfield, Nathan M. 9 Martelli, Bruno 8 Burton, Benjamin A. 7 Hodgson, Craig D. 6 Fominykh, Evgeny Anatol’evich 6 Rubinstein, J. Hyam 5 Agol, Ian 5 Neumann, Walter David 5 Tarkaev, Vladimir Viktorovich 5 Vesnin, Andrei Yu. 4 Calegari, Danny Matthew Cornelius 4 Cavicchioli, Alberto 4 Gabai, David 4 Heard, Damian 4 Meyerhoff, Robert 4 Reid, Alan W. 4 Segerman, Henry 4 Telloni, Agnese Ilaria 4 Weeks, Jeffrey R. 3 Adams, Colin C. 3 Cristofori, Paola 3 Floyd, William J. 3 Garoufalidis, Stavros 3 Kang, Ensil 3 Lackenby, Marc 3 Mednykh, Aleksandr Dmitrievich 3 Milley, Peter 3 Motegi, Kimihiko 3 Reboucas, Marcelo J. 2 Amendola, Gennaro 2 Baker, Kenneth L. 2 Callahan, Jason 2 Callahan, Patrick J. 2 Cannon, James W. 2 Cornish, Neil J. 2 Culler, Marc 2 Eudave-Muñoz, Mario 2 Fagundes, Helio V. 2 Frigerio, Roberto 2 Goodman, Oliver A. 2 Hoffman, Neil R. 2 Ichihara, Kazuhiro 2 Inoue, Kaiki Taro 2 Kabaya, Yuichi 2 Matignon, Daniel 2 Mattman, Thomas W. 2 Miyazaki, Katura 2 Mulazzani, Michele 2 Parry, Walter R. 2 Pervova, Ekaterina 2 Purcell, Jessica Shepherd 2 Sakuma, Makoto 2 Schleimer, Saul 2 Shalen, Peter B. 2 Starkman, Glenn D. 2 Tavakol, R. K. 2 Thurston, William Paul 2 Tillmann, Stephan 2 Yang, Jun 2 Zickert, Christian K. 1 Aaber, John W. 1 Aitchison, Iain Roderick 1 Anderson, James W. 1 Armas-Sanabria, Lorena 1 Aurich, Ralf 1 Baker, Mark D. 1 Baldwin, John A. 1 Bandieri, Paola 1 Battista, Ludovico 1 Birman, Joan S. 1 Bond, John Richard 1 Boyd, David William 1 Brezin, Eva 1 Brinkmann, Peter 1 Brock, Jeffrey F. 1 Budney, Ryan David 1 Bugbee, John 1 Button, Jack Oliver 1 Byrne, Rosemary 1 Calegari, Frank 1 Canary, Richard D. 1 Champanerkar, Abhijit 1 Chesebro, Eric 1 Chinburg, Ted 1 Colestock, A. 1 Comar, Timothy D. 1 Conner, Gregory R. 1 Cooper, Daryl 1 Coulson, David 1 da Costa, S. S. 1 Deruelle, Arnaud 1 Doleshal, Brandy 1 Dowty, James G. 1 Faigin, Keith A. 1 Francaviglia, Stefano 1 Friedl, Stefan 1 Friedman, Eduardo C. 1 Futer, David 1 Gagliardi, Carlo ...and 91 more Authors
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### Cited in 54 Serials

 20 Experimental Mathematics 20 Algebraic & Geometric Topology 11 Geometry & Topology 10 Topology and its Applications 9 Classical and Quantum Gravity 8 Transactions of the American Mathematical Society 7 Journal of Knot Theory and its Ramifications 5 Geometriae Dedicata 5 Proceedings of the American Mathematical Society 4 Journal of the American Mathematical Society 3 Chaos, Solitons and Fractals 3 Conformal Geometry and Dynamics 3 Proceedings of the Steklov Institute of Mathematics 3 Journal of Topology 2 General Relativity and Gravitation 2 Mathematical Notes 2 Mathematics of Computation 2 Journal of Geometry and Physics 2 Osaka Journal of Mathematics 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Siberian Mathematical Journal 2 Communications in Analysis and Geometry 1 Astronomy and Astrophysics 1 Discrete Mathematics 1 Physics Reports 1 Russian Mathematical Surveys 1 The Mathematical Intelligencer 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Commentarii Mathematici Helvetici 1 Duke Mathematical Journal 1 Inventiones Mathematicae 1 Journal of Combinatorial Theory. Series A 1 Journal of Differential Geometry 1 Mathematische Nachrichten 1 Memoirs of the American Mathematical Society 1 Michigan Mathematical Journal 1 Results in Mathematics 1 Tokyo Journal of Mathematics 1 Acta Mathematica Hungarica 1 IMRN. International Mathematics Research Notices 1 Bulletin of the American Mathematical Society. New Series 1 Expositiones Mathematicae 1 Topology Proceedings 1 Mathematical Research Letters 1 Boletín de la Sociedad Matemática Mexicana. Third Series 1 Electronic Research Announcements of the American Mathematical Society 1 Transformation Groups 1 The Ramanujan Journal 1 Progress of Theoretical Physics 1 Milan Journal of Mathematics 1 Mediterranean Journal of Mathematics 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Vestnik Yuzhno-Ural’skogo Gosudarstvennogo Universiteta. Seriya Matematika. Mekhanika. Fizika 1 Discrete Mathematics and its Applications
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### Cited in 24 Fields

 147 Manifolds and cell complexes (57-XX) 12 Group theory and generalizations (20-XX) 12 Relativity and gravitational theory (83-XX) 10 Differential geometry (53-XX) 9 Functions of a complex variable (30-XX) 6 Number theory (11-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Combinatorics (05-XX) 5 Convex and discrete geometry (52-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Geometry (51-XX) 3 $$K$$-theory (19-XX) 3 Topological groups, Lie groups (22-XX) 3 Numerical analysis (65-XX) 3 Astronomy and astrophysics (85-XX) 2 Computer science (68-XX) 2 Quantum theory (81-XX) 1 Commutative algebra (13-XX) 1 Nonassociative rings and algebras (17-XX) 1 Special functions (33-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Operations research, mathematical programming (90-XX)