Regina Calculation Engine
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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 NTriangulation * | threeSphere () |
Returns a one-tetrahedron triangulation of the 3-sphere. More... | |
static NTriangulation * | bingsHouse () |
Returns the two-tetrahedron triangulation of the 3-sphere that is dual to Bing's house with two rooms. More... | |
static NTriangulation * | s2xs1 () |
Returns a two-tetrahedron triangulation of the product space S^2 x S^1 . More... | |
static NTriangulation * | rp2xs1 () |
Returns a three-tetrahedron triangulation of the non-orientable product space RP^2 x S^1 . More... | |
static NTriangulation * | rp3rp3 () |
Returns a triangulation of the connected sum RP^3 # RP^3 . More... | |
static NTriangulation * | lens8_3 () |
Returns the minimal triangulation of the lens space L(8,3) . More... | |
static NTriangulation * | poincareHomologySphere () |
Returns the five-tetrahedron triangulation of the Poincare homology sphere. More... | |
static NTriangulation * | weeks () |
Returns a nine-tetrahedron minimal triangulation of the Weeks manifold. More... | |
static NTriangulation * | weberSeifert () |
Returns a one-vertex triangulation of the Weber-Seifert dodecahedral space. More... | |
static NTriangulation * | seifertWeber () |
Returns a one-vertex triangulation of the Weber-Seifert dodecahedral space. More... | |
static NTriangulation * | smallClosedOrblHyperbolic () |
Returns the nine-tetrahedron closed orientable hyperbolic 3-manifold with volume 0.94270736. More... | |
static NTriangulation * | smallClosedNonOrblHyperbolic () |
Returns the eleven-tetrahedron closed non-orientable hyperbolic 3-manifold with volume 2.02988321. More... | |
static NTriangulation * | sphere600 () |
Returns the boundary 3-sphere of the regular 600-cell. More... | |
Finite Bounded Triangulations | |
static NTriangulation * | lst3_4_7 () |
Returns the three-tetrahedron layered solid torus LST(3,4,7) . More... | |
static NTriangulation * | solidKleinBottle () |
Returns a triangulation of the solid Klein bottle. More... | |
Ideal Triangulations | |
static NTriangulation * | figureEightKnotComplement () |
Returns a two-tetrahedron ideal triangulation of the figure eight knot complement. More... | |
static NTriangulation * | trefoilKnotComplement () |
Returns a two-tetrahedron ideal triangulation of the trefoil knot complement. More... | |
static NTriangulation * | whiteheadLinkComplement () |
Returns a four-tetrahedron ideal triangulation of the Whitehead link complement. More... | |
static NTriangulation * | gieseking () |
Returns the one-tetrahedron ideal triangulation of the non-orientable Gieseking manifold. More... | |
static NTriangulation * | cuspedGenusTwoTorus () |
Returns a triangulation of a solid genus two torus with a cusped boundary. More... | |
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.
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Returns the two-tetrahedron triangulation of the 3-sphere that is dual to Bing's house with two rooms.
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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.
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Returns a two-tetrahedron ideal triangulation of the figure eight knot complement.
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Returns the one-tetrahedron ideal triangulation of the non-orientable Gieseking manifold.
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Returns the minimal triangulation of the lens space L(8,3)
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Returns the three-tetrahedron layered solid torus LST(3,4,7)
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Returns the five-tetrahedron triangulation of the Poincare homology sphere.
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Returns a three-tetrahedron triangulation of the non-orientable product space RP^2 x S^1
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Returns a triangulation of the connected sum RP^3 # RP^3
.
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Returns a two-tetrahedron triangulation of the product space S^2 x S^1
.
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Returns a one-vertex triangulation of the Weber-Seifert dodecahedral space.
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Returns the eleven-tetrahedron closed non-orientable hyperbolic 3-manifold with volume 2.02988321.
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Returns the nine-tetrahedron closed orientable hyperbolic 3-manifold with volume 0.94270736.
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Returns a triangulation of the solid Klein bottle.
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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
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Returns a one-tetrahedron triangulation of the 3-sphere.
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Returns a two-tetrahedron ideal triangulation of the trefoil knot complement.
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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.
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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).
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Returns a four-tetrahedron ideal triangulation of the Whitehead link complement.