Regina Calculation Engine
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Represents a triangular pillow L(3,1) component of a triangulation. More...
#include <subcomplex/l31pillow.h>
Public Member Functions | |
virtual | ~L31Pillow () |
Destroys this structure. More... | |
L31Pillow * | clone () const |
Returns a newly created clone of this structure. More... | |
Tetrahedron< 3 > * | tetrahedron (int whichTet) const |
Returns one of the two tetrahedra involved in this structure. More... | |
unsigned | interiorVertex (int whichTet) const |
Returns the vertex number of the given tetrahedron corresponding to the degree three vertex in the interior of the triangular pillow. More... | |
Manifold * | manifold () const override |
Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented. More... | |
AbelianGroup * | homology () const override |
Returns the expected first homology group of this triangulation, if such a routine has been implemented. More... | |
std::ostream & | writeName (std::ostream &out) const override |
Writes the name of this triangulation as a human-readable string to the given output stream. More... | |
std::ostream & | writeTeXName (std::ostream &out) const override |
Writes the name of this triangulation in TeX format to the given output stream. More... | |
void | writeTextLong (std::ostream &out) const override |
Writes a detailed text representation of this object to the given output stream. More... | |
std::string | name () const |
Returns the name of this specific triangulation as a human-readable string. More... | |
std::string | TeXName () const |
Returns the name of this specific triangulation in TeX format. More... | |
AbelianGroup * | homologyH1 () const |
Returns the expected first homology group of this triangulation, if such a routine has been implemented. More... | |
virtual void | writeTextShort (std::ostream &out) const |
Writes a short text representation of this object to the given output stream. More... | |
std::string | str () const |
Returns a short text representation of this object. More... | |
std::string | utf8 () const |
Returns a short text representation of this object using unicode characters. More... | |
std::string | detail () const |
Returns a detailed text representation of this object. More... | |
Static Public Member Functions | |
static L31Pillow * | isL31Pillow (const Component< 3 > *comp) |
Determines if the given triangulation component is a triangular pillow L(3,1). More... | |
static StandardTriangulation * | isStandardTriangulation (Component< 3 > *component) |
Determines whether the given component represents one of the standard triangulations understood by Regina. More... | |
static StandardTriangulation * | isStandardTriangulation (Triangulation< 3 > *tri) |
Determines whether the given triangulation represents one of the standard triangulations understood by Regina. More... | |
Represents a triangular pillow L(3,1) component of a triangulation.
A triangular pillow L(3,1) is a two-tetrahedron two-vertex triangulation of the lens space L(3,1) formed as follows.
A triangular pillow is formed from two tetrahedra with a single degree three vertex in the interior of the pillow. The two boundary triangles of this pillow are then identified with a one-third twist.
All optional StandardTriangulation routines are implemented for this class.
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inherited |
Returns a detailed text representation of this object.
This text may span many lines, and should provide the user with all the information they could want. It should be human-readable, should not contain extremely long lines (which cause problems for users reading the output in a terminal), and should end with a final newline. There are no restrictions on the underlying character set.
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inherited |
Returns a short text representation of this object.
This text should be human-readable, should fit on a single line, and should not end with a newline. Where possible, it should use plain ASCII characters.
str()
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inherited |
Returns a short text representation of this object using unicode characters.
Like str(), this text should be human-readable, should fit on a single line, and should not end with a newline. In addition, it may use unicode characters to make the output more pleasant to read. This string will be encoded in UTF-8.