Regina Calculation Engine

This class offers routines for constructing sample 3manifold triangulations of various types. More...
#include <triangulation/nexampletriangulation.h>
Static Public Member Functions  
Closed Triangulations  
static NTriangulation *  threeSphere () 
Returns a onetetrahedron triangulation of the 3sphere. More...  
static NTriangulation *  bingsHouse () 
Returns the twotetrahedron triangulation of the 3sphere that is dual to Bing's house with two rooms. More...  
static NTriangulation *  s2xs1 () 
Returns a twotetrahedron triangulation of the product space S^2 x S^1 . More...  
static NTriangulation *  rp2xs1 () 
Returns a threetetrahedron triangulation of the nonorientable 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 fivetetrahedron triangulation of the Poincare homology sphere. More...  
static NTriangulation *  weeks () 
Returns a ninetetrahedron minimal triangulation of the Weeks manifold. More...  
static NTriangulation *  weberSeifert () 
Returns a onevertex triangulation of the WeberSeifert dodecahedral space. More...  
static REGINA_DEPRECATED NTriangulation *  seifertWeber () 
Returns a onevertex triangulation of the WeberSeifert dodecahedral space. More...  
static NTriangulation *  smallClosedOrblHyperbolic () 
Returns the ninetetrahedron closed orientable hyperbolic 3manifold with volume 0.94270736. More...  
static NTriangulation *  smallClosedNonOrblHyperbolic () 
Returns the eleventetrahedron closed nonorientable hyperbolic 3manifold with volume 2.02988321. More...  
static NTriangulation *  sphere600 () 
Returns the boundary 3sphere of the regular 600cell. More...  
Finite Bounded Triangulations  
static REGINA_DEPRECATED NTriangulation *  lst3_4_7 () 
Deprecated routine that returns the threetetrahedron 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 twotetrahedron ideal triangulation of the figure eight knot complement. More...  
static REGINA_DEPRECATED NTriangulation *  figureEightKnotComplement () 
Deprecated function that teturns a twotetrahedron ideal triangulation of the figure eight knot complement. More...  
static NTriangulation *  trefoil () 
Returns a twotetrahedron ideal triangulation of the trefoil knot complement. More...  
static REGINA_DEPRECATED NTriangulation *  trefoilKnotComplement () 
Deprecated function that returns a twotetrahedron ideal triangulation of the trefoil knot complement. More...  
static NTriangulation *  whiteheadLink () 
Returns a fourtetrahedron ideal triangulation of the Whitehead link complement. More...  
static REGINA_DEPRECATED NTriangulation *  whiteheadLinkComplement () 
Deprecated function that returns a fourtetrahedron ideal triangulation of the Whitehead link complement. More...  
static NTriangulation *  gieseking () 
Returns the onetetrahedron ideal triangulation of the nonorientable 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 3manifold 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 preexisting 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.

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

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.

static 
Returns a twotetrahedron ideal triangulation of the figure eight knot complement.

inlinestatic 
Deprecated function that teturns a twotetrahedron ideal triangulation of the figure eight knot complement.

static 
Returns the onetetrahedron ideal triangulation of the nonorientable Gieseking manifold.

static 
Returns a triangulation of the lens space L(p,q)
.
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. 

static 
Deprecated routine that returns the minimal triangulation of the lens space L(8,3)
.

static 
Returns the layered solid torus LST(a,b,c)
.
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. 

static 
Deprecated routine that returns the threetetrahedron layered solid torus LST(3,4,7)
.

static 
Returns the fivetetrahedron triangulation of the Poincare homology sphere.

static 
Returns a threetetrahedron triangulation of the nonorientable product space RP^2 x S^1
.

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

static 
Returns a twotetrahedron triangulation of the product space S^2 x S^1
.

static 
Returns a onevertex triangulation of the WeberSeifert dodecahedral space.

static 
Returns the eleventetrahedron closed nonorientable hyperbolic 3manifold with volume 2.02988321.

static 
Returns the ninetetrahedron closed orientable hyperbolic 3manifold with volume 0.94270736.

static 
Returns a triangulation of the solid Klein bottle.

static 
Returns the boundary 3sphere of the regular 600cell.
This is a triangulation of the 3sphere that is a simplicial complex, and in which every edge has degree five.
The triangulation was extracted from the BenedettiLutz library of triangulations. See: http://page.math.tuberlin.de/~lutz/stellar/library_of_triangulations.html

static 
Returns a onetetrahedron triangulation of the 3sphere.

static 
Returns a twotetrahedron ideal triangulation of the trefoil knot complement.

inlinestatic 
Deprecated function that returns a twotetrahedron ideal triangulation of the trefoil knot complement.

static 
Returns a onevertex triangulation of the WeberSeifert dodecahedral space.
This 3manifold is described in "Die beiden Dodekaederraume", C. Weber and H. Seifert, Math. Z. 37 (1933), no. 1, 237253. The triangulation returned by this routine (with 23 tetrahedra) is given in "The WeberSeifert dodecahedral space is nonHaken", Benjamin A. Burton, J. Hyam Rubinstein and Stephan Tillmann, Trans. Amer. Math. Soc. 364:2 (2012), pp. 911932.

static 
Returns a ninetetrahedron minimal triangulation of the Weeks manifold.
The Weeks manifold is the smallestvolume closed hyperbolic 3manifold, 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).

static 
Returns a fourtetrahedron ideal triangulation of the Whitehead link complement.

inlinestatic 
Deprecated function that returns a fourtetrahedron ideal triangulation of the Whitehead link complement.