Regina Calculation Engine
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A specific six-tetrahedron NTxICore triangulation that does not fit neatly into other families. More...
#include <subcomplex/ntxicore.h>
Public Member Functions | |
NTxIParallelCore () | |
Creates a new copy of this T x I triangulation. | |
std::ostream & | writeName (std::ostream &out) const |
Writes the name of this specific triangulation of T x I to the given output stream. | |
std::ostream & | writeTeXName (std::ostream &out) const |
Writes the name of this specific triangulation of T x I in TeX format to the given output stream. |
A specific six-tetrahedron NTxICore triangulation that does not fit neatly into other families.
This triangulation contains the fewest possible number of tetrahedra (NTxICore triangulations are not seen below six tetrahedra). It is referred to as T_6^1
in the paper "Structures of small closed
non-orientable 3-manifold triangulations", Benjamin A. Burton, J. Knot Theory Ramifications 16 (2007), 545--574. In Regina it is given the name T_6*
, to avoid confusion with the different NTxIDiagonalCore triangulation T_6:1
.
The triangulations of the upper and lower boundary tori are completely parallel (and in particular, the upper and lower alpha curves are parallel, as are the upper and lower beta curves).
For reference, the central torus of this triangulation is depicted below. The left and right sides of the diagram are identified, as are the top and bottom. The four triangles u0, u1, w0 and w1 provide the boundary faces of the overall triangulation, with the upper boundary coned out from triangles u0 and u1 and the lower boundary coned out from triangles w0 and w1. In each boundary, u0 or w0 gives the first boundary face and u1 or w1 gives the second. The directions of the corresponding alpha and beta curves are are also included.
Creates a new copy of this T x I
triangulation.
std::ostream & regina::NTxIParallelCore::writeName | ( | std::ostream & | out | ) | const [inline, virtual] |
Writes the name of this specific triangulation of T x I
to the given output stream.
The name will be written as a human-readable string.
out | the output stream to which to write. |
Implements regina::NTxICore.
std::ostream & regina::NTxIParallelCore::writeTeXName | ( | std::ostream & | out | ) | const [inline, virtual] |
Writes the name of this specific triangulation of T x I
in TeX format to the given output stream.
No leading or trailing dollar signs will be written.
out | the output stream to which to write. |
Implements regina::NTxICore.