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| SatCube (const SatCube &cloneMe) |
| Constructs a clone of the given block structure. More...
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virtual SatBlock * | clone () const |
| Returns a newly created clone of this saturated block structure. More...
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virtual void | adjustSFS (SFSpace &sfs, bool reflect) const |
| Adjusts the given Seifert fibred space to insert the contents of this saturated block. More...
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virtual void | writeTextShort (std::ostream &out) const |
| Writes a short text representation of this object to the given output stream. More...
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virtual void | writeAbbr (std::ostream &out, bool tex=false) const |
| Writes an abbreviated name or symbol for this block to the given output stream. More...
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unsigned | nAnnuli () const |
| Returns the number of annuli on the boundary of this saturated block. More...
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const SatAnnulus & | annulus (unsigned which) const |
| Returns details of the requested annulus on the boundary of this saturated block. More...
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bool | twistedBoundary () const |
| Is the ring of boundary annuli twisted to form a long Mobius strip? More...
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bool | hasAdjacentBlock (unsigned whichAnnulus) const |
| Returns whether there is another saturated block listed as being adjacent to the given boundary annulus of this block. More...
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SatBlock * | adjacentBlock (unsigned whichAnnulus) const |
| Returns the saturated block listed as being adjacent to the given boundary annulus of this block. More...
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unsigned | adjacentAnnulus (unsigned whichAnnulus) const |
| Returns which specific annulus of the adjacent block is listed as being adjacent to the given boundary annulus of this block. More...
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bool | adjacentReflected (unsigned whichAnnulus) const |
| Returns whether the adjacency along the given boundary annulus of this block is reflected. More...
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bool | adjacentBackwards (unsigned whichAnnulus) const |
| Returns whether the adjacency along the given boundary annulus of this block is backwards. More...
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void | setAdjacent (unsigned whichAnnulus, SatBlock *adjBlock, unsigned adjAnnulus, bool adjReflected, bool adjBackwards) |
| Lists the given saturated block as being adjacent to the given boundary annulus of this block. More...
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virtual void | transform (const Triangulation< 3 > *originalTri, const Isomorphism< 3 > *iso, Triangulation< 3 > *newTri) |
| Adjusts the structure of this block according to the given isomorphism between triangulations. More...
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void | nextBoundaryAnnulus (unsigned thisAnnulus, SatBlock *&nextBlock, unsigned &nextAnnulus, bool &refVert, bool &refHoriz, bool followPrev) |
| Finds the next (or previous) boundary annulus around from this, treating all adjacent blocks as part of a single large saturated region. More...
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std::string | abbr (bool tex=false) const |
| Returns an abbreviated name or symbol for this block. More...
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bool | operator< (const SatBlock &compare) const |
| Implements a consistent ordering of saturated blocks. More...
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virtual void | writeTextLong (std::ostream &out) const |
| Writes a detailed text representation of this object to the given output stream. More...
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std::string | str () const |
| Returns a short text representation of this object. More...
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std::string | utf8 () const |
| Returns a short text representation of this object using unicode characters. More...
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std::string | detail () const |
| Returns a detailed text representation of this object. More...
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static bool | isBad (Tetrahedron< 3 > *t, const TetList &list) |
| Determines whether the given tetrahedron is contained within the given list. More...
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template<class List > |
static bool | isBad (Tetrahedron< 3 > *t, const List &list) |
| Determines whether the given tetrahedron is contained within the given list. More...
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static bool | notUnique (Tetrahedron< 3 > *test) |
| Determines whether the given tetrahedron pointer is null. More...
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static bool | notUnique (Tetrahedron< 3 > *test, Tetrahedron< 3 > *other1) |
| Determines whether the given tetrahedron pointer is null or equal to another from the given list. More...
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static bool | notUnique (Tetrahedron< 3 > *test, Tetrahedron< 3 > *other1, Tetrahedron< 3 > *other2) |
| Determines whether the given tetrahedron pointer is null or equal to another from the given list. More...
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static bool | notUnique (Tetrahedron< 3 > *test, Tetrahedron< 3 > *other1, Tetrahedron< 3 > *other2, Tetrahedron< 3 > *other3) |
| Determines whether the given tetrahedron pointer is null or equal to another from the given list. More...
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static bool | notUnique (Tetrahedron< 3 > *test, Tetrahedron< 3 > *other1, Tetrahedron< 3 > *other2, Tetrahedron< 3 > *other3, Tetrahedron< 3 > *other4) |
| Determines whether the given tetrahedron pointer is null or equal to another from the given list. More...
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A saturated block that is a six-tetrahedron cube.
There are several ways of triangulating a cube with six tetrahedra; the specific method used here is illustrated in the diagram below (where the top face of the cube is identified with the bottom).
Note that none of the four tetrahedra that meet the boundary annuli touch each other, and that each of these four boundary tetrahedra meet both central tetrahedra. Note also that (unlike other triangulations) this cube cannot be split vertically into two triangular prisms.