Regina Calculation Engine
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Offers routines for constructing a variety of sample 3-dimensional triangulations. More...
#include <triangulation/example3.h>
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... | |
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.
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staticinherited |
Bounded Triangulations.
Returns a one-simplex triangulation of the dim-ball.
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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.
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staticinherited |
Returns the standard (dim+2)-simplex triangulation of the dim-sphere as the boundary of a (dim+1)-simplex.
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staticinherited |
Closed Triangulations.
Returns a two-simplex triangulation of the dim-sphere.
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staticinherited |
Returns a two-simplex triangulation of the product space S^(dim-1) x S^1
.
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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.
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staticinherited |
Returns a two-simplex triangulation of the twisted product space S^(dim-1) x~ S^1
.