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/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2025, 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. *
* *
* As an exception, when this program is distributed through (i) the *
* App Store by Apple Inc.; (ii) the Mac App Store by Apple Inc.; or *
* (iii) Google Play by Google Inc., then that store may impose any *
* digital rights management, device limits and/or redistribution *
* restrictions that are required by its terms of service. *
* *
* 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, see <https://www.gnu.org/licenses/>. *
* *
**************************************************************************/
#include <algorithm>
#include "algebra/abeliangroup.h"
#include "manifold/handlebody.h"
#include "manifold/lensspace.h"
#include "manifold/simplesurfacebundle.h"
#include "subcomplex/trivialtri.h"
#include "triangulation/dim3.h"
namespace regina {
std::unique_ptr<TrivialTri> TrivialTri::recognise(const Component<3>* comp) {
// Since the triangulations are so small we can use census results
// to recognise the triangulations by properties alone.
// Are there any boundary components?
if (! comp->isClosed()) {
if (comp->countBoundaryComponents() == 1) {
// We have precisely one boundary component.
BoundaryComponent<3>* bc = comp->boundaryComponent(0);
if (! bc->isIdeal()) {
// The boundary component includes boundary triangles.
// Look for a one-tetrahedron ball.
if (comp->size() == 1) {
if (bc->countTriangles() == 4)
return std::unique_ptr<TrivialTri>(
new TrivialTri(BALL_4_VERTEX));
if (bc->countTriangles() == 2 && comp->countVertices() == 3)
return std::unique_ptr<TrivialTri>(
new TrivialTri(BALL_3_VERTEX));
}
}
}
// Not recognised.
return nullptr;
}
// Otherwise we are dealing with a closed component.
// Before we do our validity check, make sure the number of
// tetrahedra is in the supported range.
if (comp->size() > 3)
return nullptr;
// Is the triangulation valid?
// Since the triangulations is closed we know that the vertices are
// valid; all that remains is to check the edges.
size_t nEdges = comp->countEdges();
for (size_t i = 0; i < nEdges; i++)
if (! comp->edge(i)->isValid())
return nullptr;
// Test for the specific triangulations that we know about.
if (comp->size() == 2) {
if (comp->isOrientable()) {
if (comp->countVertices() == 4) {
// There's only one closed valid two-tetrahedron
// four-vertex orientable triangulation.
return std::unique_ptr<TrivialTri>(
new TrivialTri(SPHERE_4_VERTEX));
} else if (comp->countVertices() == 2) {
// The census says we have one of three triangulations:
// - cMcabbgig : S^3, edge degrees 6 4 1 1
// - cPcbbbaai : L(3,1), edge degrees 6 2 2 2
// - cPcbbbahh : RP^2, edge degrees 4 4 2 2
//
// The only one of these that *this* class is interested
// in detecting is the L(3,1).
for (const Edge<3>* e : comp->edges())
if (e->degree() == 4)
return nullptr;
return std::unique_ptr<TrivialTri>(new TrivialTri(L31_PILLOW));
}
} else {
// There's only one closed valid two-tetrahedron non-orientable
// triangulation.
return std::unique_ptr<TrivialTri>(new TrivialTri(N2));
}
return nullptr;
}
if (comp->size() == 3) {
if (! comp->isOrientable()) {
// If the triangulation is valid and the edge degrees
// are 2,4,4,6 then we have N(3,1) or N(3,2).
// All of the vertices are valid since there are no boundary
// triangles; we thus only need to check the edges.
if (comp->countEdges() != 4)
return nullptr;
size_t degree[4];
for (int i = 0; i < 4; i++)
degree[i] = comp->edge(i)->degree();
std::sort(degree, degree + 4);
if (degree[0] == 2 && degree[1] == 4 && degree[2] == 6 &&
degree[3] == 6) {
// We have N(3,1) or N(3,2)!
// Search for Mobius band triangles.
size_t nTriangles = comp->countTriangles();
for (size_t i = 0; i < nTriangles; i++)
if (comp->triangle(i)->formsMobiusBand())
return std::unique_ptr<TrivialTri>(
new TrivialTri(N3_2));
return std::unique_ptr<TrivialTri>(new TrivialTri(N3_1));
}
}
}
return nullptr;
}
std::unique_ptr<Manifold> TrivialTri::manifold() const {
switch (type_) {
case SPHERE_4_VERTEX:
return std::make_unique<LensSpace>(1, 0);
case BALL_3_VERTEX:
case BALL_4_VERTEX:
return std::make_unique<Handlebody>(0);
case L31_PILLOW:
return std::make_unique<LensSpace>(3, 1);
case N2:
return std::make_unique<SimpleSurfaceBundle>(
SimpleSurfaceBundle::S2xS1_TWISTED);
case N3_1:
case N3_2:
return std::make_unique<SimpleSurfaceBundle>(
SimpleSurfaceBundle::RP2xS1);
default:
return nullptr;
}
}
AbelianGroup TrivialTri::homology() const {
switch (type_) {
case L31_PILLOW:
return AbelianGroup(0, {3});
case N2:
return AbelianGroup(1);
case N3_1:
case N3_2:
return AbelianGroup(1, {2});
default:
return AbelianGroup();
}
}
std::ostream& TrivialTri::writeName(std::ostream& out) const {
switch (type_) {
case SPHERE_4_VERTEX:
out << "S3 (4-vtx)"; break;
case BALL_3_VERTEX:
out << "B3 (3-vtx)"; break;
case BALL_4_VERTEX:
out << "B3 (4-vtx)"; break;
case L31_PILLOW:
out << "L'(3,1)"; break;
case N2:
out << "N(2)"; break;
case N3_1:
out << "N(3,1)"; break;
case N3_2:
out << "N(3,2)"; break;
}
return out;
}
std::ostream& TrivialTri::writeTeXName(std::ostream& out) const {
switch (type_) {
case SPHERE_4_VERTEX:
out << "S^3_{v=4}"; break;
case BALL_3_VERTEX:
out << "B^3_{v=3}"; break;
case BALL_4_VERTEX:
out << "B^3_{v=4}"; break;
case L31_PILLOW:
out << "L'_{3,1}"; break;
case N2:
out << "N_{2}"; break;
case N3_1:
out << "N_{3,1}"; break;
case N3_2:
out << "N_{3,2}"; break;
}
return out;
}
void TrivialTri::writeTextLong(std::ostream& out) const {
switch (type_) {
case SPHERE_4_VERTEX:
out << "Two-tetrahedron four-vertex 3-sphere"; break;
case BALL_3_VERTEX:
out << "One-tetrahedron three-vertex ball"; break;
case BALL_4_VERTEX:
out << "One-tetrahedron four-vertex ball"; break;
case L31_PILLOW:
out << "Triangular pillow lens space L(3,1)"; break;
case N2:
out << "Non-orientable triangulation N(2)"; break;
case N3_1:
out << "Non-orientable triangulation N(3,1)"; break;
case N3_2:
out << "Non-orientable triangulation N(3,2)"; break;
}
}
} // namespace regina
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