Regina Calculation Engine
Static Public Member Functions | List of all members
regina::Example< 3 > Class Reference

Offers routines for constructing a variety of sample 3-dimensional triangulations. More...

#include <triangulation/example3.h>

Inheritance diagram for regina::Example< 3 >:
regina::detail::ExampleBase< 3 >

Static Public Member Functions

static Triangulation< dim > * sphere ()
 Closed Triangulations. More...
 
static Triangulation< dim > * simplicialSphere ()
 Returns the standard (dim+2)-simplex triangulation of the dim-sphere as the boundary of a (dim+1)-simplex. More...
 
static Triangulation< dim > * sphereBundle ()
 Returns a two-simplex triangulation of the product space S^(dim-1) x S^1. More...
 
static Triangulation< dim > * twistedSphereBundle ()
 Returns a two-simplex triangulation of the twisted product space S^(dim-1) x~ S^1. More...
 
static Triangulation< dim > * ball ()
 Bounded Triangulations. More...
 
static Triangulation< dim > * ballBundle ()
 Returns a triangulation of the product space B^(dim-1) x S^1. More...
 
static Triangulation< dim > * twistedBallBundle ()
 Returns a triangulation of the twisted product space B^(dim-1) x~ S^1. More...
 
Closed Triangulations
static Triangulation< 3 > * threeSphere ()
 Returns a one-tetrahedron triangulation of the 3-sphere. More...
 
static Triangulation< 3 > * bingsHouse ()
 Returns the two-tetrahedron triangulation of the 3-sphere that is dual to Bing's house with two rooms. More...
 
static Triangulation< 3 > * s2xs1 ()
 Returns a two-tetrahedron triangulation of the product space S^2 x S^1. More...
 
static Triangulation< 3 > * rp2xs1 ()
 Returns a three-tetrahedron triangulation of the non-orientable product space RP^2 x S^1. More...
 
static Triangulation< 3 > * rp3rp3 ()
 Returns a triangulation of the connected sum RP^3 # RP^3. More...
 
static Triangulation< 3 > * lens (size_t p, size_t q)
 Returns a triangulation of the lens space L(p,q). More...
 
static Triangulation< 3 > * poincareHomologySphere ()
 Returns the five-tetrahedron triangulation of the Poincare homology sphere. More...
 
static Triangulation< 3 > * weeks ()
 Returns a nine-tetrahedron minimal triangulation of the Weeks manifold. More...
 
static Triangulation< 3 > * weberSeifert ()
 Returns a one-vertex triangulation of the Weber-Seifert dodecahedral space. More...
 
static Triangulation< 3 > * smallClosedOrblHyperbolic ()
 Returns the nine-tetrahedron closed orientable hyperbolic 3-manifold with volume 0.94270736. More...
 
static Triangulation< 3 > * smallClosedNonOrblHyperbolic ()
 Returns the eleven-tetrahedron closed non-orientable hyperbolic 3-manifold with volume 2.02988321. More...
 
static Triangulation< 3 > * sphere600 ()
 Returns the boundary 3-sphere of the regular 600-cell. More...
 
Finite Bounded Triangulations
static Triangulation< 3 > * lst (size_t a, size_t b)
 Returns the layered solid torus LST(a,b,c). More...
 
static Triangulation< 3 > * solidKleinBottle ()
 Returns a triangulation of the solid Klein bottle. More...
 
Ideal Triangulations
static Triangulation< 3 > * figureEight ()
 Returns a two-tetrahedron ideal triangulation of the figure eight knot complement. More...
 
static Triangulation< 3 > * trefoil ()
 Returns a two-tetrahedron ideal triangulation of the trefoil knot complement. More...
 
static Triangulation< 3 > * whiteheadLink ()
 Returns a four-tetrahedron ideal triangulation of the Whitehead link complement. More...
 
static Triangulation< 3 > * gieseking ()
 Returns the one-tetrahedron ideal triangulation of the non-orientable Gieseking manifold. More...
 
static Triangulation< 3 > * cuspedGenusTwoTorus ()
 Returns a triangulation of a solid genus two torus with a cusped boundary. More...
 

Detailed Description

Offers routines for constructing a variety of sample 3-dimensional triangulations.

This is a specialisation of the generic Example class template; see the Example template documentation for a general overview of how the example triangulation classes work.

This 3-dimensional specialisation offers significant extra functionality, by providing several more hard-coded and parameterised constructions.

Member Function Documentation

◆ ball()

Triangulation< dim > * regina::detail::ExampleBase< dim >::ball
staticinherited

Bounded Triangulations.

Returns a one-simplex triangulation of the dim-ball.

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

◆ ballBundle()

Triangulation< dim > * regina::detail::ExampleBase< dim >::ballBundle
staticinherited

Returns a triangulation of the product space B^(dim-1) x S^1.

This will use one simplex in odd dimensions, or two simplices in even dimensions.

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

◆ simplicialSphere()

Triangulation< dim > * regina::detail::ExampleBase< dim >::simplicialSphere
staticinherited

Returns the standard (dim+2)-simplex triangulation of the dim-sphere as the boundary of a (dim+1)-simplex.

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

◆ sphere()

Triangulation< dim > * regina::detail::ExampleBase< dim >::sphere
staticinherited

Closed Triangulations.

Returns a two-simplex triangulation of the dim-sphere.

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

◆ sphereBundle()

Triangulation< dim > * regina::detail::ExampleBase< dim >::sphereBundle
staticinherited

Returns a two-simplex triangulation of the product space S^(dim-1) x S^1.

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

◆ twistedBallBundle()

Triangulation< dim > * regina::detail::ExampleBase< dim >::twistedBallBundle
staticinherited

Returns a triangulation of the twisted product space B^(dim-1) x~ S^1.

This will use one simplex in even dimensions, or two simplices in odd dimensions.

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

◆ twistedSphereBundle()

Triangulation< dim > * regina::detail::ExampleBase< dim >::twistedSphereBundle
staticinherited

Returns a two-simplex triangulation of the twisted product space S^(dim-1) x~ S^1.

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 © 1999-2021, The Regina development team
This software is released under the GNU General Public License, with some additional permissions; see the source code for details.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@maths.uq.edu.au).