Regina Calculation Engine
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regina::NExampleTriangulation Class Reference

This class offers routines for constructing sample 3-manifold triangulations of various types. More...

#include <triangulation/nexampletriangulation.h>

Static Public Member Functions

Closed Triangulations
static NTriangulationthreeSphere ()
 Returns a one-tetrahedron triangulation of the 3-sphere. More...
 
static NTriangulationbingsHouse ()
 Returns the two-tetrahedron triangulation of the 3-sphere that is dual to Bing's house with two rooms. More...
 
static NTriangulations2xs1 ()
 Returns a two-tetrahedron triangulation of the product space S^2 x S^1. More...
 
static NTriangulationrp2xs1 ()
 Returns a three-tetrahedron triangulation of the non-orientable product space RP^2 x S^1. More...
 
static NTriangulationrp3rp3 ()
 Returns a triangulation of the connected sum RP^3 # RP^3. More...
 
static NTriangulationlens8_3 ()
 Returns the minimal triangulation of the lens space L(8,3). More...
 
static NTriangulationpoincareHomologySphere ()
 Returns the five-tetrahedron triangulation of the Poincare homology sphere. More...
 
static NTriangulationweeks ()
 Returns a nine-tetrahedron minimal triangulation of the Weeks manifold. More...
 
static NTriangulationweberSeifert ()
 Returns a one-vertex triangulation of the Weber-Seifert dodecahedral space. More...
 
static NTriangulationseifertWeber ()
 Returns a one-vertex triangulation of the Weber-Seifert dodecahedral space. More...
 
static NTriangulationsmallClosedOrblHyperbolic ()
 Returns the nine-tetrahedron closed orientable hyperbolic 3-manifold with volume 0.94270736. More...
 
static NTriangulationsmallClosedNonOrblHyperbolic ()
 Returns the eleven-tetrahedron closed non-orientable hyperbolic 3-manifold with volume 2.02988321. More...
 
static NTriangulationsphere600 ()
 Returns the boundary 3-sphere of the regular 600-cell. More...
 
Finite Bounded Triangulations
static NTriangulationlst3_4_7 ()
 Returns the three-tetrahedron layered solid torus LST(3,4,7). More...
 
static NTriangulationsolidKleinBottle ()
 Returns a triangulation of the solid Klein bottle. More...
 
Ideal Triangulations
static NTriangulationfigureEightKnotComplement ()
 Returns a two-tetrahedron ideal triangulation of the figure eight knot complement. More...
 
static NTriangulationtrefoilKnotComplement ()
 Returns a two-tetrahedron ideal triangulation of the trefoil knot complement. More...
 
static NTriangulationwhiteheadLinkComplement ()
 Returns a four-tetrahedron ideal triangulation of the Whitehead link complement. More...
 
static NTriangulationgieseking ()
 Returns the one-tetrahedron ideal triangulation of the non-orientable Gieseking manifold. More...
 
static NTriangulationcuspedGenusTwoTorus ()
 Returns a triangulation of a solid genus two torus with a cusped boundary. More...
 

Detailed Description

This class offers routines for constructing sample 3-manifold triangulations of various types.

These triangulations may be useful for testing new code, or for simply getting a feel for how Regina works.

The sample triangulations offered here may prove especially useful in Regina's scripting interface, where working with pre-existing files is more complicated than in the GUI.

Note that each of these routines constructs a new triangulation from scratch. It is up to the caller of each routine to destroy the triangulation that is returned.

Member Function Documentation

static NTriangulation* regina::NExampleTriangulation::bingsHouse ( )
static

Returns the two-tetrahedron triangulation of the 3-sphere that is dual to Bing's house with two rooms.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.
static NTriangulation* regina::NExampleTriangulation::cuspedGenusTwoTorus ( )
static

Returns a triangulation of a solid genus two torus with a cusped boundary.

This triangulation has one internal finite vertex and one genus two ideal vertex.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.
static NTriangulation* regina::NExampleTriangulation::figureEightKnotComplement ( )
static

Returns a two-tetrahedron ideal triangulation of the figure eight knot complement.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.
static NTriangulation* regina::NExampleTriangulation::gieseking ( )
static

Returns the one-tetrahedron ideal triangulation of the non-orientable Gieseking manifold.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.
static NTriangulation* regina::NExampleTriangulation::lens8_3 ( )
static

Returns the minimal triangulation of the lens space L(8,3).

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.
static NTriangulation* regina::NExampleTriangulation::lst3_4_7 ( )
static

Returns the three-tetrahedron layered solid torus LST(3,4,7).

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.
static NTriangulation* regina::NExampleTriangulation::poincareHomologySphere ( )
static

Returns the five-tetrahedron triangulation of the Poincare homology sphere.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.
static NTriangulation* regina::NExampleTriangulation::rp2xs1 ( )
static

Returns a three-tetrahedron triangulation of the non-orientable product space RP^2 x S^1.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.
static NTriangulation* regina::NExampleTriangulation::rp3rp3 ( )
static

Returns a triangulation of the connected sum RP^3 # RP^3.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.
static NTriangulation* regina::NExampleTriangulation::s2xs1 ( )
static

Returns a two-tetrahedron triangulation of the product space S^2 x S^1.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.
static NTriangulation* regina::NExampleTriangulation::seifertWeber ( )
static

Returns a one-vertex triangulation of the Weber-Seifert dodecahedral space.

Deprecated:
This routine is now called weberSeifert(), for consistency with Weber and Seifert's original paper. The old name seifertWeber() has been kept for backward compatibility, but will be removed in a future version of Regina.
Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.
static NTriangulation* regina::NExampleTriangulation::smallClosedNonOrblHyperbolic ( )
static

Returns the eleven-tetrahedron closed non-orientable hyperbolic 3-manifold with volume 2.02988321.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.
static NTriangulation* regina::NExampleTriangulation::smallClosedOrblHyperbolic ( )
static

Returns the nine-tetrahedron closed orientable hyperbolic 3-manifold with volume 0.94270736.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.
static NTriangulation* regina::NExampleTriangulation::solidKleinBottle ( )
static

Returns a triangulation of the solid Klein bottle.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.
static NTriangulation* regina::NExampleTriangulation::sphere600 ( )
static

Returns the boundary 3-sphere of the regular 600-cell.

This is a triangulation of the 3-sphere that is a simplicial complex, and in which every edge has degree five.

The triangulation was extracted from the Benedetti-Lutz library of triangulations. See: http://page.math.tu-berlin.de/~lutz/stellar/library_of_triangulations.html

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.
static NTriangulation* regina::NExampleTriangulation::threeSphere ( )
static

Returns a one-tetrahedron triangulation of the 3-sphere.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.
static NTriangulation* regina::NExampleTriangulation::trefoilKnotComplement ( )
static

Returns a two-tetrahedron ideal triangulation of the trefoil knot complement.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.
static NTriangulation* regina::NExampleTriangulation::weberSeifert ( )
static

Returns a one-vertex triangulation of the Weber-Seifert dodecahedral space.

This 3-manifold is described in "Die beiden Dodekaederraume", C. Weber and H. Seifert, Math. Z. 37 (1933), no. 1, 237-253. The triangulation returned by this routine (with 23 tetrahedra) is given in "The Weber-Seifert dodecahedral space is non-Haken", Benjamin A. Burton, J. Hyam Rubinstein and Stephan Tillmann, Trans. Amer. Math. Soc. 364:2 (2012), pp. 911-932.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.
static NTriangulation* regina::NExampleTriangulation::weeks ( )
static

Returns a nine-tetrahedron minimal triangulation of the Weeks manifold.

The Weeks manifold is the smallest-volume closed hyperbolic 3-manifold, with a volume of roughly 0.9427. Note that there are nine minimal triangulations of the Weeks manifold (of course this routine returns just one).

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.
static NTriangulation* regina::NExampleTriangulation::whiteheadLinkComplement ( )
static

Returns a four-tetrahedron ideal triangulation of the Whitehead link complement.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.

The documentation for this class was generated from the following file:

Copyright © 1999-2014, The Regina development team
This software is released under the GNU General Public License, with some additional permissions; see the source code for details.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@debian.org).