regina::NExampleTriangulation Class Reference
[Triangulations]

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

#include <nexampletriangulation.h>

List of all members.

Static Public Member Functions

Closed Triangulations



static NTriangulationthreeSphere ()
 Returns a one-tetrahedron triangulation of the 3-sphere.
static NTriangulations2xs1 ()
 Returns a two-tetrahedron triangulation of the product space S^2 x S^1.
static NTriangulationrp2xs1 ()
 Returns a three-tetrahedron triangulation of the non-orientable product space RP^2 x S^1.
static NTriangulationrp3rp3 ()
 Returns a triangulation of the connected sum RP^3 # RP^3.
static NTriangulationlens8_3 ()
 Returns the minimal triangulation of the lens space L(8,3).
static NTriangulationpoincareHomologySphere ()
 Returns the five-tetrahedron triangulation of the Poincare homology sphere.
static NTriangulationseifertWeber ()
 Returns a one-vertex triangulation of the Seifert-Weber dodecahedral space.
static NTriangulationsmallClosedOrblHyperbolic ()
 Returns the nine-tetrahedron closed orientable hyperbolic 3-manifold with volume 0.94270736.
static NTriangulationsmallClosedNonOrblHyperbolic ()
 Returns the eleven-tetrahedron closed non-orientable hyperbolic 3-manifold with volume 2.02988321.
Finite Bounded Triangulations

(end: Closed Triangulations)



static NTriangulationlst3_4_7 ()
 Returns the three-tetrahedron layered solid torus LST(3,4,7).
static NTriangulationsolidKleinBottle ()
 Returns a triangulation of the solid Klein bottle.
Ideal Triangulations

(end: Finite Bounded Triangulations)



static NTriangulationfigureEightKnotComplement ()
 Returns a two-tetrahedron ideal triangulation of the figure eight knot complement.
static NTriangulationwhiteheadLinkComplement ()
 Returns a four-tetrahedron ideal triangulation of the Whitehead link complement.
static NTriangulationgieseking ()
 Returns the one-tetrahedron ideal triangulation of the non-orientable Gieseking manifold.
static NTriangulationcuspedGenusTwoTorus ()
 Returns a triangulation of a solid genus two torus with a cusped boundary.

Detailed Description

This class offers routines for constructing sample 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::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 Seifert-Weber dodecahedral space.

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::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::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 © 1999-2009, Ben Burton
This software is released under the GNU General Public License.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@debian.org).