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/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2008, Ben Burton *
* For further details contact Ben Burton (bab@debian.org). *
* *
* This program is free software; you can redistribute it and/or *
* modify it under the terms of the GNU General Public License as *
* published by the Free Software Foundation; either version 2 of the *
* License, or (at your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, but *
* WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
* General Public License for more details. *
* *
* You should have received a copy of the GNU General Public *
* License along with this program; if not, write to the Free *
* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, *
* MA 02110-1301, USA. *
* *
**************************************************************************/
/* end stub */
#include "split/nsignature.h"
#include "triangulation/nexampletriangulation.h"
#include "triangulation/ntriangulation.h"
namespace {
static const int poincareAdj[5][4] = {
{ 1, 2, 3, 4},
{ 0, 2, 3, 4},
{ 0, 1, 3, 4},
{ 0, 1, 2, 4},
{ 0, 1, 2, 3}
};
static const int poincareGluings[5][4][4] = {
{ { 0, 2, 3, 1 }, { 3, 0, 1, 2 }, { 2, 3, 0, 1 }, { 3, 1, 2, 0 } },
{ { 0, 3, 1, 2 }, { 2, 1, 3, 0 }, { 3, 0, 1, 2 }, { 2, 3, 0, 1 } },
{ { 1, 2, 3, 0 }, { 3, 1, 0, 2 }, { 1, 3, 2, 0 }, { 3, 0, 1, 2 } },
{ { 2, 3, 0, 1 }, { 1, 2, 3, 0 }, { 3, 0, 2, 1 }, { 1, 2, 0, 3 } },
{ { 3, 1, 2, 0 }, { 2, 3, 0, 1 }, { 1, 2, 3, 0 }, { 2, 0, 1, 3 } }
};
static const int closedOrHypAdj[9][4] = {
{ 6, 8, 2, 8 },
{ 6, 8, 3, 7 },
{ 7, 0, 3, 4 },
{ 1, 5, 5, 2 },
{ 2, 6, 5, 7 },
{ 3, 8, 3, 4 },
{ 0, 4, 7, 1 },
{ 1, 4, 2, 6 },
{ 1, 0, 5, 0 }
};
static const int closedOrHypGluings[9][4][4] = {
{ { 0, 1, 3, 2 }, { 3, 1, 2, 0 }, { 0, 2, 1, 3 }, { 0, 2, 1, 3 } },
{ { 3, 1, 2, 0 }, { 1, 0, 2, 3 }, { 3, 2, 0, 1 }, { 2, 3, 1, 0 } },
{ { 2, 0, 3, 1 }, { 0, 2, 1, 3 }, { 0, 1, 3, 2 }, { 3, 1, 2, 0 } },
{ { 2, 3, 1, 0 }, { 3, 2, 0, 1 }, { 2, 1, 0, 3 }, { 0, 1, 3, 2 } },
{ { 3, 1, 2, 0 }, { 0, 1, 3, 2 }, { 0, 1, 3, 2 }, { 3, 2, 0, 1 } },
{ { 2, 1, 0, 3 }, { 0, 2, 1, 3 }, { 2, 3, 1, 0 }, { 0, 1, 3, 2 } },
{ { 0, 1, 3, 2 }, { 0, 1, 3, 2 }, { 0, 1, 3, 2 }, { 3, 1, 2, 0 } },
{ { 3, 2, 0, 1 }, { 2, 3, 1, 0 }, { 1, 3, 0, 2 }, { 0, 1, 3, 2 } },
{ { 1, 0, 2, 3 }, { 3, 1, 2, 0 }, { 0, 2, 1, 3 }, { 0, 2, 1, 3 } }
};
static const int closedNorHypAdj[11][4] = {
{ 8, 2, 8, 2 },
{ 5, 3, 2, 9 },
{ 1, 4, 0, 0 },
{ 6, 1, 4, 6 },
{ 10, 2, 10, 3 },
{ 7, 7, 6, 1 },
{ 8, 3, 3, 5 },
{ 5, 9, 8, 5 },
{ 0, 0, 6, 7 },
{ 10, 10, 1, 7 },
{ 9, 4, 4, 9 }
};
static const int closedNorHypGluings[11][4][4] = {
{ { 1, 3, 2, 0 }, { 0, 3, 2, 1 }, { 2, 1, 0, 3 }, { 3, 1, 0, 2 } },
{ { 3, 0, 1, 2 }, { 3, 1, 0, 2 }, { 2, 1, 0, 3 }, { 1, 0, 3, 2 } },
{ { 2, 1, 0, 3 }, { 3, 1, 2, 0 }, { 2, 1, 3, 0 }, { 0, 3, 2, 1 } },
{ { 2, 1, 3, 0 }, { 2, 1, 3, 0 }, { 2, 0, 3, 1 }, { 0, 3, 2, 1 } },
{ { 2, 1, 0, 3 }, { 3, 1, 2, 0 }, { 3, 2, 1, 0 }, { 1, 3, 0, 2 } },
{ { 3, 1, 2, 0 }, { 1, 0, 3, 2 }, { 0, 1, 3, 2 }, { 1, 2, 3, 0 } },
{ { 2, 1, 0, 3 }, { 0, 3, 2, 1 }, { 3, 1, 0, 2 }, { 0, 1, 3, 2 } },
{ { 1, 0, 3, 2 }, { 0, 3, 2, 1 }, { 0, 1, 3, 2 }, { 3, 1, 2, 0 } },
{ { 2, 1, 0, 3 }, { 3, 0, 2, 1 }, { 2, 1, 0, 3 }, { 0, 1, 3, 2 } },
{ { 3, 1, 2, 0 }, { 2, 0, 1, 3 }, { 1, 0, 3, 2 }, { 0, 3, 2, 1 } },
{ { 1, 2, 0, 3 }, { 3, 2, 1, 0 }, { 2, 1, 0, 3 }, { 3, 1, 2, 0 } }
};
static const int whiteheadAdj[4][4] = {
{ 3, 2, 1, 3},
{ 3, 2, 2, 0},
{ 1, 3, 0, 1},
{ 2, 0, 0, 1}
};
static const int whiteheadGluings[4][4][4] = {
{ { 2, 3, 1, 0 }, { 3, 2, 0, 1 }, { 0, 1, 3, 2 }, { 3, 2, 0, 1 } },
{ { 3, 2, 0, 1 }, { 2, 3, 1, 0 }, { 3, 2, 0, 1 }, { 0, 1, 3, 2 } },
{ { 2, 3, 1, 0 }, { 1, 0, 2, 3 }, { 2, 3, 1, 0 }, { 3, 2, 0, 1 } },
{ { 1, 0, 2, 3 }, { 2, 3, 1, 0 }, { 3, 2, 0, 1 }, { 2, 3, 1, 0 } }
};
}
namespace regina {
NTriangulation* NExampleTriangulation::threeSphere() {
NTriangulation* ans = new NTriangulation();
ans->setPacketLabel("3-sphere");
ans->insertLayeredLensSpace(1, 0);
return ans;
}
NTriangulation* NExampleTriangulation::s2xs1() {
NTriangulation* ans = new NTriangulation();
ans->setPacketLabel("S2 x S1");
ans->insertLayeredLensSpace(0, 1);
return ans;
}
NTriangulation* NExampleTriangulation::rp2xs1() {
// Section 3.5.1 of Benjamin Burton's PhD thesis describes how to
// construct RP^2 x S^1 by identifying the boundary faces of a
// solid Klein bottle.
NTriangulation* ans = solidKleinBottle();
ans->setPacketLabel("RP2 x S1");
NTetrahedron* r = ans->getTetrahedron(0);
NTetrahedron* t = ans->getTetrahedron(2);
r->joinTo(1, t, NPerm(2, 3, 0, 1));
r->joinTo(3, t, NPerm(2, 3, 0, 1));
ans->gluingsHaveChanged();
return ans;
}
NTriangulation* NExampleTriangulation::rp3rp3() {
// This can be generated as the enclosing triangulation of a splitting
// surface, as described in chapter 4 of Benjamin Burton's PhD thesis.
NSignature* sig = NSignature::parse("aabccd.b.d");
NTriangulation* ans = sig->triangulate();
ans->setPacketLabel("RP3 # RP3");
delete sig;
return ans;
}
NTriangulation* NExampleTriangulation::lens8_3() {
NTriangulation* ans = new NTriangulation();
ans->setPacketLabel("L(8,3)");
ans->insertLayeredLensSpace(8, 3);
return ans;
}
NTriangulation* NExampleTriangulation::poincareHomologySphere() {
NTriangulation* ans = new NTriangulation();
ans->setPacketLabel("Poincare homology sphere");
ans->insertConstruction(5, poincareAdj, poincareGluings);
return ans;
}
NTriangulation* NExampleTriangulation::seifertWeber() {
NTriangulation* ans = new NTriangulation();
ans->setPacketLabel("Seifert-Weber dodecahedral space");
// Bah. Dehydration strings are somewhat impenetrable,
// but the alternative is 23 lines of hard-coded tetrahedron gluings.
//
// This triangulation was constructed by building a 60-tetrahedron
// dodecahedron and identifying opposite faces with a 3/10 twist,
// and then simplifying down to one vertex and 23 tetrahedra.
ans->insertRehydration(
"xppphocgaeaaahimmnkontspmuuqrsvuwtvwwxwjjsvvcxxjjqattdwworrko");
return ans;
}
NTriangulation* NExampleTriangulation::smallClosedOrblHyperbolic() {
NTriangulation* ans = new NTriangulation();
ans->setPacketLabel("Closed orientable hyperbolic 3-manifold");
ans->insertConstruction(9, closedOrHypAdj, closedOrHypGluings);
return ans;
}
NTriangulation* NExampleTriangulation::smallClosedNonOrblHyperbolic() {
NTriangulation* ans = new NTriangulation();
ans->setPacketLabel("Closed non-orientable hyperbolic 3-manifold");
ans->insertConstruction(11, closedNorHypAdj, closedNorHypGluings);
return ans;
}
NTriangulation* NExampleTriangulation::lst3_4_7() {
NTriangulation* ans = new NTriangulation();
ans->setPacketLabel("Layered solid torus");
ans->insertLayeredSolidTorus(3, 4);
return ans;
}
NTriangulation* NExampleTriangulation::solidKleinBottle() {
NTriangulation* ans = new NTriangulation();
ans->setPacketLabel("Solid Klein bottle");
// A three-tetrahedron solid Klein bottle is described in section
// 3.5.1 of Benjamin Burton's PhD thesis.
NTetrahedron* r = new NTetrahedron();
NTetrahedron* s = new NTetrahedron();
NTetrahedron* t = new NTetrahedron();
s->joinTo(0, r, NPerm(0, 1, 2, 3));
s->joinTo(3, r, NPerm(3, 0, 1, 2));
s->joinTo(1, t, NPerm(3, 0, 1, 2));
s->joinTo(2, t, NPerm(0, 1, 2, 3));
ans->addTetrahedron(r);
ans->addTetrahedron(s);
ans->addTetrahedron(t);
return ans;
}
NTriangulation* NExampleTriangulation::figureEightKnotComplement() {
NTriangulation* ans = new NTriangulation();
ans->setPacketLabel("Figure eight knot complement");
// The two-tetrahedron figure eight knot complement is described at
// the beginning of chapter 8 of Richard Rannard's PhD thesis.
NTetrahedron* r = new NTetrahedron();
NTetrahedron* s = new NTetrahedron();
r->joinTo(0, s, NPerm(1, 3, 0, 2));
r->joinTo(1, s, NPerm(2, 0, 3, 1));
r->joinTo(2, s, NPerm(0, 3, 2, 1));
r->joinTo(3, s, NPerm(2, 1, 0, 3));
ans->addTetrahedron(r);
ans->addTetrahedron(s);
return ans;
}
NTriangulation* NExampleTriangulation::whiteheadLinkComplement() {
NTriangulation* ans = new NTriangulation();
ans->setPacketLabel("Whitehead link complement");
ans->insertConstruction(4, whiteheadAdj, whiteheadGluings);
return ans;
}
NTriangulation* NExampleTriangulation::gieseking() {
NTriangulation* ans = new NTriangulation();
ans->setPacketLabel("Gieseking manifold");
NTetrahedron* r = new NTetrahedron();
r->joinTo(0, r, NPerm(1, 2, 0, 3));
r->joinTo(2, r, NPerm(0, 2, 3, 1));
ans->addTetrahedron(r);
return ans;
}
NTriangulation* NExampleTriangulation::cuspedGenusTwoTorus() {
NTriangulation* ans = new NTriangulation();
ans->setPacketLabel("Cusped genus two solid torus");
// We create this by first constructing an ordinary solid genus two
// torus and then converting the real boundary to an ideal vertex.
NTetrahedron* r = new NTetrahedron();
NTetrahedron* s = new NTetrahedron();
NTetrahedron* t = new NTetrahedron();
NTetrahedron* u = new NTetrahedron();
r->joinTo(0, s, NPerm());
r->joinTo(1, t, NPerm(1, 2, 3, 0));
r->joinTo(2, u, NPerm(1, 0, 3, 2));
s->joinTo(3, t, NPerm());
t->joinTo(1, u, NPerm());
ans->addTetrahedron(r);
ans->addTetrahedron(s);
ans->addTetrahedron(t);
ans->addTetrahedron(u);
ans->finiteToIdeal();
return ans;
}
} // namespace regina
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