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 REGINA_DEPRECATED NTriangulation * | lens8_3 () |
Deprecated routine that returns the minimal triangulation of the lens space L(8,3) . More... | |
static NTriangulation * | lens (size_t p, size_t q) |
Returns a triangulation of the lens space L(p,q) . 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 REGINA_DEPRECATED 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 REGINA_DEPRECATED NTriangulation * | lst3_4_7 () |
Deprecated routine that returns the three-tetrahedron layered solid torus LST(3,4,7) . More... | |
static NTriangulation * | lst (size_t a, size_t b) |
Returns the layered solid torus LST(a,b,c) . More... | |
static NTriangulation * | solidKleinBottle () |
Returns a triangulation of the solid Klein bottle. More... | |
Ideal Triangulations | |
static NTriangulation * | figureEight () |
Returns a two-tetrahedron ideal triangulation of the figure eight knot complement. More... | |
static REGINA_DEPRECATED NTriangulation * | figureEightKnotComplement () |
Deprecated function that teturns a two-tetrahedron ideal triangulation of the figure eight knot complement. More... | |
static NTriangulation * | trefoil () |
Returns a two-tetrahedron ideal triangulation of the trefoil knot complement. More... | |
static REGINA_DEPRECATED NTriangulation * | trefoilKnotComplement () |
Deprecated function that returns a two-tetrahedron ideal triangulation of the trefoil knot complement. More... | |
static NTriangulation * | whiteheadLink () |
Returns a four-tetrahedron ideal triangulation of the Whitehead link complement. More... | |
static REGINA_DEPRECATED NTriangulation * | whiteheadLinkComplement () |
Deprecated function that 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.
All of the methods in this class will assign an appropriate packet label to the triangulation that they return.
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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inlinestatic |
Deprecated function that teturns 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 a triangulation of the lens space L(p,q)
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The triangulation uses a layered lens space, which is conjectured (but not proven in all cases) to be the triangulation requiring the fewest tetrahedra.
p | a parameter of the desired lens space. |
q | a parameter of the desired lens space. |
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Deprecated routine that returns the minimal triangulation of the lens space L(8,3)
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Returns the layered solid torus LST(a,b,c)
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This is a parameterised triangulation of the solid torus. It has two boundary triangles and three boundary edges, and the meridional disc of the solid torus cuts these boundary edges a, b and c times respectively.
Only the parameters a and b are passed as arguments to this routine. The third parameter c will be deduced automatically as c = (a + b).
a | the first parameter of the layered solid torus. |
b | the second parameter of the layered solid torus. |
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Deprecated routine that 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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inlinestatic |
Deprecated function that 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.
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inlinestatic |
Deprecated function that returns a four-tetrahedron ideal triangulation of the Whitehead link complement.