Regina Calculation Engine
regina::NExampleTriangulation Class Reference

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

#include <triangulation/nexampletriangulation.h>

List of all members.

Static Public Member Functions

Closed Triangulations
static NTriangulationthreeSphere ()
 Returns a one-tetrahedron triangulation of the 3-sphere.
static NTriangulationbingsHouse ()
 Returns the two-tetrahedron triangulation of the 3-sphere that is dual to Bing's house with two rooms.
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 NTriangulationweeks ()
 Returns a nine-tetrahedron minimal triangulation of the Weeks manifold.
static NTriangulationweberSeifert ()
 Returns a one-vertex triangulation of the Weber-Seifert dodecahedral space.
static NTriangulationseifertWeber ()
 Returns a one-vertex triangulation of the Weber-Seifert 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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Returns a triangulation of the solid Klein bottle.

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

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

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

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.

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.

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 © 1999-2012, The Regina development team
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).