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<html>
<head>
<link rel="stylesheet" type="text/css" href="regina.css">
<title>Regina - Supporting Data</title>
</head>
<body bgcolor="#FFFFFF" text="#000000"
link="#0000EE" vlink="#551A8B" alink="#FF0000">
<h1><a name="contents">Regina – Supporting Data</a></h1>
<p>
<table class="contentswrapper" cellspacing=0>
<tbody>
<tr><td valign="top">
<table class="contents" cellspacing=0><tbody>
<tr><td><a href="#knots">Classical knot tables</a></td></tr>
<tr><td><a href="#virtual">Virtual knot tables</a></td></tr>
<tr><td><a href="#census">3-manifold census data</a></td></tr>
<tr><td><a href="#weber-seifert">Weber-Seifert dodecahedral space</a></td></tr>
<tr><td><a href="index.html">Back to main page ...</a></td></tr>
</tbody></table>
</td></tr>
</tbody>
</table>
<h2><a name="knots">Classical knot tables</a></h2>
Regina includes native support for knots and links.
If you wish to play with some smaller examples, you can open Regina and
select <i>Open Example</i> → <i>Prime Knots</i> from the menu.
<p>
If you want more, then here you can
download the tables of all 352,152,252 prime non-trivial knots with up to
19 crossings.
<p>
The tables are plain text CSV (comma-separated value) files which you can
load into a spreadsheet and/or process with a text editor, and have been
compressed with <tt>bzip2</tt>. The fields include:
<p>
<ul>
<li><p><b>name:</b> The name of the knot, using a naming scheme
specific to these tables.
An example name is <tt>12nh_137</tt>.
In general the name is of the form <i>c[an][tsh]_k</i>, where:
<ul><li><i>c</i> is the number of crossings;</li>
<li><i>[an]</i> indicates whether the knot is alternating or
non-alternating;</li>
<li><i>[tsh]</i> indicates whether the knot is
a torus, satellite or hyperbolic knot;</li>
<li><i>k</i> is a positive integer that sorts the knots
within each of these classes.</li></ul>
<p>
The torus and satellite knots are sorted according to their
structure. The hyperbolic knots are sorted <i>roughly</i> by
volume, but take care—although the distinctness and hyperbolicity
of the knots are proven using exact computation, the final sorting order
is based on approximate volume computation only.
</li>
<li><p><b>knot_sig:</b> The knot diagram, expressed as a native Regina
knot signature. An example signature (for the knot <tt>7ah_5</tt>)
is <tt>habcadebcfgedgfvvb-Za</tt>.
<i>Knot signatures</i> uniquely identify a diagram on
the 2-sphere up to relabelling, reflection, rotation and/or reversal.
In Regina 5.2 or later you can reconstruct a knot diagram
from its signature through the GUI, or by
calling <tt>Link.fromKnotSig()</tt> in python.
<li><p><b>dt_code:</b> The knot diagram, expressed as an alphabetical
Dowker-Thistlethwaite (DT) code An example DT code (again for the knot
<tt>7ah_5</tt>) is <tt>fdgeacb</tt>.
<li><p><b>dt_name:</b> Identifies the knot in other online databases such as
<a href="http://www.indiana.edu/~knotinfo/">Knotinfo</a> and
<!--a href="http://pzacad.pitzer.edu/~jhoste/HosteWebPages/kntscp.html">Knotscape</a-->
<a href="http://www.math.utk.edu/~morwen/knotscape.html">Knotscape</a>
(this field only appears in the tables for
≤ 12 crossings). This field uses the
Dowker-Thistlethwaite naming convention, where knots are numbered
according to their minimal DT codes.
<li><p><b>structure:</b> Gives the full structure of a torus or
satellite knot (this field does not appear in the hyperbolic tables).
An example is <tt>Trefoil[-3/2]</tt>, indicating a
satellite formed by inserting the rational tangle -3/2 into the double
of the right-hand trefoil. See the paper below for a full explanation
of what the various structure descriptions mean.
</ul>
<p>
<b>Citation:</b> If you wish to cite this data, please reference:
<ul>
<li>Benjamin A. Burton,
<a href="https://drops.dagstuhl.de/opus/volltexte/2020/12183/"><i>The next 350 million knots</i></a>,
36th International Symposium on Computational Geometry (SoCG 2020)
(S. Cabello, D.Z. Chen, eds.),
Leibniz Int. Proc. Inform., vol. 164,
Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2020,
pp. 25:1–25:17.</li>
</ul>
<p>
<a href="http://www.maths.uq.edu.au/~bab/knots/all_3-12.tar.bz2">Download all 3–12 crossing knots at once</a> (56 KB)<br>
<a href="http://www.maths.uq.edu.au/~bab/knots/all_13-16.tar.bz2">Download all 13–16 crossing knots at once</a> (41 MB)<br>
Download individual tables (up to 19 crossings) below:
<p>
<table cellspacing=0 border=0 class="data"><tbody>
<tr>
<th class="first" colspan=2>Crossings</th>
<th>Torus</th>
<th>Satellite</th>
<th colspan=2>Hyperbolic</th>
</tr>
<tr>
<td class="knotcross">3</td><td>alternating</td>
<td class="knotcountsmall"><a href="http://www.maths.uq.edu.au/~bab/knots/3a-torus.csv.bz2">1 knot</a></td>
<td class="knotcountsmall">—</td>
<td class="knotcount">—</td><td> </td>
</tr>
<tr>
<td class="knotcross">4</td><td>alternating</td>
<td class="knotcountsmall">—</td>
<td class="knotcountsmall">—</td>
<td class="knotcount"><a href="http://www.maths.uq.edu.au/~bab/knots/4a-hyp.csv.bz2">1 knot</a></td><td class="knotsize"> </td>
</tr>
<tr>
<td class="knotcross">5</td><td>alternating</td>
<td class="knotcountsmall"><a href="http://www.maths.uq.edu.au/~bab/knots/5a-torus.csv.bz2">1 knot</a></td>
<td class="knotcountsmall">—</td>
<td class="knotcount"><a href="http://www.maths.uq.edu.au/~bab/knots/5a-hyp.csv.bz2">1 knot</a></td><td class="knotsize"> </td>
</tr>
<tr>
<td class="knotcross">6</td><td>alternating</td>
<td class="knotcountsmall">—</td>
<td class="knotcountsmall">—</td>
<td class="knotcount"><a href="http://www.maths.uq.edu.au/~bab/knots/6a-hyp.csv.bz2">3 knots</a></td><td class="knotsize"> </td>
</tr>
<tr>
<td class="knotcross">7</td><td>alternating</td>
<td class="knotcountsmall"><a href="http://www.maths.uq.edu.au/~bab/knots/7a-torus.csv.bz2">1 knot</a></td>
<td class="knotcountsmall">—</td>
<td class="knotcount"><a href="http://www.maths.uq.edu.au/~bab/knots/7a-hyp.csv.bz2">6 knots</a></td><td class="knotsize"> </td>
</tr>
<tr>
<td class="knotcross" rowspan=2>8</td><td class="knotalt">alternating</td>
<td class="knotcountuppersmall">—</td>
<td class="knotcountuppersmall">—</td>
<td class="knotcountupper"><a href="http://www.maths.uq.edu.au/~bab/knots/8a-hyp.csv.bz2">18 knots</a></td><td class="knotsizeupper"> </td>
</tr><tr>
<td>non-alternating</td>
<td class="knotcountsmall"><a href="http://www.maths.uq.edu.au/~bab/knots/8n-torus.csv.bz2">1 knot</a></td>
<td class="knotcountsmall">—</td>
<td class="knotcount"><a href="http://www.maths.uq.edu.au/~bab/knots/8n-hyp.csv.bz2">2 knots</a></td><td class="knotsize"> </td>
</tr>
<tr>
<td class="knotcross" rowspan=2>9</td><td class="knotalt">alternating</td>
<td class="knotcountuppersmall"><a href="http://www.maths.uq.edu.au/~bab/knots/9a-torus.csv.bz2">1 knot</a></td>
<td class="knotcountuppersmall">—</td>
<td class="knotcountupper"><a href="http://www.maths.uq.edu.au/~bab/knots/9a-hyp.csv.bz2">40 knots</a></td><td class="knotsizeupper"> </td>
</tr><tr>
<td>non-alternating</td>
<td class="knotcountsmall">—</td>
<td class="knotcountsmall">—</td>
<td class="knotcount"><a href="http://www.maths.uq.edu.au/~bab/knots/9n-hyp.csv.bz2">8 knots</a></td><td class="knotsize"> </td>
</tr>
<tr>
<td class="knotcross" rowspan=2>10</td><td class="knotalt">alternating</td>
<td class="knotcountuppersmall">—</td>
<td class="knotcountuppersmall">—</td>
<td class="knotcountupper"><a href="http://www.maths.uq.edu.au/~bab/knots/10a-hyp.csv.bz2">123 knots</a></td><td class="knotsizeupper"> </td>
</tr><tr>
<td>non-alternating</td>
<td class="knotcountsmall"><a href="http://www.maths.uq.edu.au/~bab/knots/10n-torus.csv.bz2">1 knot</a></td>
<td class="knotcountsmall">—</td>
<td class="knotcount"><a href="http://www.maths.uq.edu.au/~bab/knots/10n-hyp.csv.bz2">41 knots</a></td><td class="knotsize"> </td>
</tr>
<tr>
<td class="knotcross" rowspan=2>11</td><td class="knotalt">alternating</td>
<td class="knotcountuppersmall"><a href="http://www.maths.uq.edu.au/~bab/knots/11a-torus.csv.bz2">1 knot</a></td>
<td class="knotcountuppersmall">—</td>
<td class="knotcountupper"><a href="http://www.maths.uq.edu.au/~bab/knots/11a-hyp.csv.bz2">366 knots</a></td><td class="knotsizeupper"> </td>
</tr><tr>
<td>non-alternating</td>
<td class="knotcountsmall">—</td>
<td class="knotcountsmall">—</td>
<td class="knotcount"><a href="http://www.maths.uq.edu.au/~bab/knots/11n-hyp.csv.bz2">185 knots</a></td><td class="knotsize"> </td>
</tr>
<tr>
<td class="knotcross" rowspan=2>12</td><td class="knotalt">alternating</td>
<td class="knotcountuppersmall">—</td>
<td class="knotcountuppersmall">—</td>
<td class="knotcountupper"><a href="http://www.maths.uq.edu.au/~bab/knots/12a-hyp.csv.bz2">1,288 knots</a></td><td class="knotsizeupper"> </td>
</tr><tr>
<td>non-alternating</td>
<td class="knotcountsmall">—</td>
<td class="knotcountsmall">—</td>
<td class="knotcount"><a href="http://www.maths.uq.edu.au/~bab/knots/12n-hyp.csv.bz2">888 knots</a></td><td class="knotsize"> </td>
</tr>
<tr>
<td class="knotcross" rowspan=2>13</td><td class="knotalt">alternating</td>
<td class="knotcountuppersmall"><a href="http://www.maths.uq.edu.au/~bab/knots/13a-torus.csv.bz2">1 knot</a></td>
<td class="knotcountuppersmall">—</td>
<td class="knotcountupper"><a href="http://www.maths.uq.edu.au/~bab/knots/13a-hyp.csv.bz2">4,877 knots</a></td><td class="knotsizeupper"> </td>
</tr><tr>
<td>non-alternating</td>
<td class="knotcountsmall">—</td>
<td class="knotcountsmall"><a href="http://www.maths.uq.edu.au/~bab/knots/13n-satellite.csv.bz2">2 knots</a></td>
<td class="knotcount"><a href="http://www.maths.uq.edu.au/~bab/knots/13n-hyp.csv.bz2">5,108 knots</a></td><td class="knotsize"> </td>
</tr>
<tr>
<td class="knotcross" rowspan=2>14</td><td class="knotalt">alternating</td>
<td class="knotcountuppersmall">—</td>
<td class="knotcountuppersmall">—</td>
<td class="knotcountupper"><a href="http://www.maths.uq.edu.au/~bab/knots/14a-hyp.csv.bz2">19,536 knots</a></td><td class="knotsizeupper"> </td>
</tr><tr>
<td>non-alternating</td>
<td class="knotcountsmall"><a href="http://www.maths.uq.edu.au/~bab/knots/14n-torus.csv.bz2">1 knot</a></td>
<td class="knotcountsmall"><a href="http://www.maths.uq.edu.au/~bab/knots/14n-satellite.csv.bz2">2 knots</a></td>
<td class="knotcount"><a href="http://www.maths.uq.edu.au/~bab/knots/14n-hyp.csv.bz2">27,433 knots</a></td><td class="knotsize"> </td>
</tr>
<tr>
<td class="knotcross" rowspan=2>15</td><td class="knotalt">alternating</td>
<td class="knotcountuppersmall"><a href="http://www.maths.uq.edu.au/~bab/knots/15a-torus.csv.bz2">1 knot</a></td>
<td class="knotcountuppersmall">—</td>
<td class="knotcountupper"><a href="http://www.maths.uq.edu.au/~bab/knots/15a-hyp.csv.bz2">85,262 knots</a></td><td class="knotsizeupper">(1.6 MB)</td>
</tr><tr>
<td>non-alternating</td>
<td class="knotcountsmall"><a href="http://www.maths.uq.edu.au/~bab/knots/15n-torus.csv.bz2">1 knot</a></td>
<td class="knotcountsmall"><a href="http://www.maths.uq.edu.au/~bab/knots/15n-satellite.csv.bz2">6 knots</a></td>
<td class="knotcount"><a href="http://www.maths.uq.edu.au/~bab/knots/15n-hyp.csv.bz2">168,023 knots</a></td><td class="knotsize">(4.0 MB)</td>
</tr>
<tr>
<td class="knotcross" rowspan=2>16</td><td class="knotalt">alternating</td>
<td class="knotcountuppersmall">—</td>
<td class="knotcountuppersmall">—</td>
<td class="knotcountupper"><a href="http://www.maths.uq.edu.au/~bab/knots/16a-hyp.csv.bz2">379,799 knots</a></td><td class="knotsizeupper">(7.9 MB)</td>
</tr><tr>
<td>non-alternating</td>
<td class="knotcountsmall"><a href="http://www.maths.uq.edu.au/~bab/knots/16n-torus.csv.bz2">1 knot</a></td>
<td class="knotcountsmall"><a href="http://www.maths.uq.edu.au/~bab/knots/16n-satellite.csv.bz2">10 knots</a></td>
<td class="knotcount"><a href="http://www.maths.uq.edu.au/~bab/knots/16n-hyp.csv.bz2">1,008,895 knots</a></td><td class="knotsize">(27 MB)</td>
</tr>
<tr>
<td class="knotcross" rowspan=2>17</td><td class="knotalt">alternating</td>
<td class="knotcountuppersmall"><a href="http://www.maths.uq.edu.au/~bab/knots/17a-torus.csv.bz2">1 knot</a></td>
<td class="knotcountuppersmall">—</td>
<td class="knotcountupper"><a href="http://www.maths.uq.edu.au/~bab/knots/17a-hyp.csv.bz2">1,769,978 knots</a></td><td class="knotsizeupper">(41 MB)</td>
</tr><tr>
<td>non-alternating</td>
<td class="knotcountsmall">—</td>
<td class="knotcountsmall"><a href="http://www.maths.uq.edu.au/~bab/knots/17n-satellite.csv.bz2">29 knots</a></td>
<td class="knotcount"><a href="http://www.maths.uq.edu.au/~bab/knots/17n-hyp.csv.bz2">6,283,385 knots</a></td><td class="knotsize">(184 MB)</td>
</tr>
<tr>
<td class="knotcross" rowspan=2>18</td><td class="knotalt">alternating</td>
<td class="knotcountuppersmall">—</td>
<td class="knotcountuppersmall">—</td>
<td class="knotcountupper"><a href="http://www.maths.uq.edu.au/~bab/knots/18a-hyp.csv.bz2">8,400,285 knots</a></td><td class="knotsizeupper">(215 MB)</td>
</tr><tr>
<td>non-alternating</td>
<td class="knotcountsmall">—</td>
<td class="knotcountsmall"><a href="http://www.maths.uq.edu.au/~bab/knots/18n-satellite.csv.bz2">86 knots</a></td>
<td class="knotcount"><a href="http://www.maths.uq.edu.au/~bab/knots/18n-hyp.csv.bz2">39,866,095 knots</a></td><td class="knotsize">(1.3 GB)</td>
</tr>
<tr>
<td class="knotcross" rowspan=2>19</td><td class="knotalt">alternating</td>
<td class="knotcountuppersmall"><a href="http://www.maths.uq.edu.au/~bab/knots/19a-torus.csv.bz2">1 knot</a></td>
<td class="knotcountuppersmall">—</td>
<td class="knotcountupper"><a href="http://www.maths.uq.edu.au/~bab/knots/19a-hyp.csv.bz2">40,619,384 knots</a></td><td class="knotsizeupper">(1.1 GB)</td>
</tr><tr>
<td>non-alternating</td>
<td class="knotcountsmall">—</td>
<td class="knotcountsmall"><a href="http://www.maths.uq.edu.au/~bab/knots/19n-satellite.csv.bz2">245 knots</a></td>
<td class="knotcount"><a href="http://www.maths.uq.edu.au/~bab/knots/19n-hyp.csv.bz2">253,510,828 knots</a></td><td class="knotsize">(8.7 GB)</td>
</tr>
</table>
<p>
<i><a href="#contents">(Back to top...)</a></i>
<h2><a name="virtual">Virtual knot tables</a></h2>
Regina 7.4 introduces support for virtual knots and links.
If you wish to play with some small examples, you can open Regina and
select <i>Open Example</i> → <i>Virtual Knots</i> from the menu.
<p>
Here you can download the tables of all 92,798 non-trivial virtual knots
with up to 6 crossings.
<p>
These virtual knots were tabulated independently using Regina.
Reflections, reversals and flips are all considered to be the same knot.
Classical knots are included also, and all knots in this census have been
certified as distinct. The knots are sorted by number of crossings,
then virtual genus, and then lexicographically by Regina's knot signature.
<p>
The tables are plain text CSV (comma-separated value) files which you can
load into a spreadsheet and/or process with a text editor, and have been
compressed with <tt>bzip2</tt>. The fields include:
<p>
<ul>
<li><p><b>name:</b> The name of the knot, using a naming scheme
specific to these tables.
An example name is <tt>v6_97</tt>; here <tt>6</tt> indicates the
number of classical crossings, and <tt>97</tt> is a positive integer
indicating the position of the knot within the tables.
</li>
<li><p><b>knot_sig:</b> The knot diagram, expressed as a native Regina
knot signature. An example signature (for the knot <tt>6_97</tt>)
is <tt>gabacdefcdbfeRu--</tt>.
<i>Knot signatures</i> uniquely identify a knot diagram up to
relabelling, reflection, rotation and/or reversal.
In Regina 7.4 or later you can reconstruct a virtual knot diagram
from its signature through the GUI, or by calling <tt>Link.fromSig()</tt>
in python.
<li><p><b>signed_gauss:</b> The knot diagram, expressed as a
signed Gauss code. An example signed Gauss code (again for the knot
<tt>6_97</tt>) is <tt>O1+O2+U1+O3+U4+O5+U6+U3+O4+U2+O6+U5+</tt>.
<li><p><b>genus:</b> The virtual genus of the knot.
This is the smallest genus closed orientable surface in which the
knot diagram can be embedded. Classical knots have virtual genus zero.
<li><p><b>green_name:</b> Identifies the knot in
<a href="https://www.math.toronto.edu/drorbn/Students/GreenJ/">Jeremy Green's
virtual knot tables</a>.
<li><p><b>classical_name:</b> For classical knots only,
this field identifies the knot in
<a href="#knots">Regina's classical knot tables</a>.
Note that some knots in these tables are <i>composite</i> classical knots,
and so will have names such as <tt>3at_1#3at_1'</tt> (indicating the
composition of the left and right trefoils).
<li><p><b>dt_name:</b> For classical knots only,
this field identifies the knot in other online databases such as
<a href="http://www.indiana.edu/~knotinfo/">Knotinfo</a> and
<!--a href="http://pzacad.pitzer.edu/~jhoste/HosteWebPages/kntscp.html">Knotscape</a-->
<a href="http://www.math.utk.edu/~morwen/knotscape.html">Knotscape</a>.
This field uses the Dowker-Thistlethwaite naming convention, where knots
are numbered according to their minimal DT codes. Again, be aware of
composite knots.
</ul>
<p>
Note that this census is smaller than Green's. This is because Green's tables
contain a duplicate pair (<tt>v6_421</tt> in these tables,
<tt>6.88185 = 6.90058</tt> in Green's).
<p>
<b>Citation:</b> If you wish to cite this data, please reference:
<ul>
<li>Benjamin A. Burton,
<i>Adventures in tabulating virtual knots</i>,
in preparation.</li>
</ul>
<p>
<a href="http://www.maths.uq.edu.au/~bab/knots/virtual_2-6.tar.bz2">Download all 2–6 crossing knots at once</a> (962 KB)<br>
Download individual tables below:
<p>
<table cellspacing=0 border=0 class="data"><tbody>
<tr>
<th class="first">Crossings</th>
<th>Knots</th>
</tr>
<tr>
<td class="knotvcross">2</td>
<td class="knotcountsmall"><a href="http://www.maths.uq.edu.au/~bab/knots/2-virtual.csv.bz2">1 knot</a></td>
</tr>
<tr>
<td class="knotvcross">3</td>
<td class="knotcountsmall"><a href="http://www.maths.uq.edu.au/~bab/knots/3-virtual.csv.bz2">7 knots</a></td>
</tr>
<tr>
<td class="knotvcross">4</td>
<td class="knotcountsmall"><a href="http://www.maths.uq.edu.au/~bab/knots/4-virtual.csv.bz2">108 knots</a></td>
</tr>
<tr>
<td class="knotvcross">5</td>
<td class="knotcountsmall"><a href="http://www.maths.uq.edu.au/~bab/knots/5-virtual.csv.bz2">2,448 knots</a></td>
</tr>
<tr>
<td class="knotvcross">6</td>
<td class="knotcountsmall"><a href="http://www.maths.uq.edu.au/~bab/knots/6-virtual.csv.bz2">90,234 knots</a></td>
</tr>
</table>
<p>
<i><a href="#contents">(Back to top...)</a></i>
<h2><a name="census">3-manifold census data</a></h2>
Regina ships with several different censuses of triangulations.
You can access most of these censuses by selecting
<i>File → Open Example</i> from Regina's main menu.
</ul>
<p>
Here you can download additional census files that are too
large to ship with Regina. You can also find the standard files
that <i>are</i> shipped, in case you have an older version of Regina
that did not include them.
<p>
You can open each of these data files directly within Regina.
Each file begins with a text packet that describes what
the census contains and where the data originally came from.
<p>
<table cellspacing=0 border=0 class="data"><tbody>
<tr>
<th class="first">Census</th>
<th>Origin</th>
<th>Download</th>
<th>Size (kB)</th>
</tr>
<tr><td class="subheading" colspan=4>Closed census</td></tr>
<tr>
<td class="first">All minimal triangulations of all closed orientable
prime 3-manifolds<br>
≤ 10 tetrahedra</td>
<td rowspan=3>Tabulated by
<a href="http://arxiv.org/abs/1101.3091">Burton</a></td>
<td><a href="census/closed-or-census.rga">closed-or-census.rga</a></td>
<td>848</td>
</tr>
<tr>
<td class="first">All minimal triangulations of all closed orientable
prime 3-manifolds<br>
≤ 11 tetrahedra <i>(too large to ship with Regina)</i></td>
<td><a href="census/closed-or-census-11.rga">closed-or-census-11.rga</a></td>
<td>1906</td>
</tr>
<tr>
<td class="first">All minimal triangulations of all closed non-orientable
P<sup>2</sup>-irreducible 3-manifolds<br>
≤ 11 tetrahedra</td>
<td><a href="census/closed-nor-census.rga">closed-nor-census.rga</a></td>
<td>537</td>
</tr>
<tr><td class="subheading" colspan=4>Closed hyperbolic census</td></tr>
<tr>
<td class="first">Smallest known closed hyperbolic 3-manifolds<br>
3000 orientable, 18 non-orientable</td>
<td rowspan=2>Tabulated
by <a href="http://projecteuclid.org/euclid.em/1048515809">Hodgson and
Weeks</a></td>
<td><a href="census/closed-hyp-census.rga">closed-hyp-census.rga</a></td>
<td>310</td>
</tr>
<tr>
<td class="first">Smallest known closed hyperbolic 3-manifolds<br>
11031 orientable, 18 non-orientable
<i>(too large to ship with Regina)</i></td>
<td><a href="census/closed-hyp-census-full.rga">closed-hyp-census-full.rga</a></td>
<td>1275</td>
</tr>
<tr><td class="subheading" colspan=4>Cusped hyperbolic census</td></tr>
<tr>
<td class="first">All minimal triangulations of all cusped hyperbolic
orientable 3-manifolds<br>
≤ 7 tetrahedra</td>
<td rowspan=4>Tabulated by
<a href="http://arxiv.org/abs/1405.2695">Burton</a></td>
<td><a href="census/cusped-hyp-or-census.rga">cusped-hyp-or-census.rga</a></td>
<td>354</td>
</tr>
<tr>
<td class="first">All minimal triangulations of all cusped hyperbolic
non-orientable 3-manifolds<br>
≤ 7 tetrahedra</td>
<td><a href="census/cusped-hyp-nor-census.rga">cusped-hyp-nor-census.rga</a></td>
<td>179</td>
</tr>
<tr>
<td class="first">All minimal triangulations of all cusped hyperbolic
orientable 3-manifolds<br>
≤ 9 tetrahedra <i>(too large to ship with Regina)</i></td>
<td><a href="census/cusped-hyp-or-census-9.rga">cusped-hyp-or-census-9.rga</a></td>
<td>7902</td>
</tr>
<tr>
<td class="first">All minimal triangulations of all cusped hyperbolic
non-orientable 3-manifolds<br>
≤ 9 tetrahedra <i>(too large to ship with Regina)</i></td>
<td><a href="census/cusped-hyp-nor-census-9.rga">cusped-hyp-nor-census-9.rga</a></td>
<td>3571</td>
</tr>
<tr><td class="subheading" colspan=4>Knot and link complements</td></tr>
<tr>
<td class="first">Christy's collection of knot complements
(≤ 11 crossings) and link complements (≤ 10 crossings)</td>
<td>Collected by Christy<br>Shipped with
<a href="http://www.ms.unimelb.edu.au/~snap">Snap 1.9</a></td>
<td><a href="census/hyp-knot-link-census.rga">hyp-knot-link-census.rga</a></td>
<td>132</td>
</tr>
</tbody></table>
<p>
In older versions of Regina, Christy's collection used to be called
“hyperbolic knot / link complements”;
however, it also contains some (but not all) non-hyperbolic cases.
It also contains the duplicate Perko pair.
<p>
<i><a href="#contents">(Back to top...)</a></i>
<h2><a name="weber-seifert">Weber-Seifert dodecahedral space</a></h2>
The <i>Weber-Seifert dodecahedral space</i> was one of the first-known
examples of a hyperbolic 3-manifold, and Thurston conjectured around 1980
that this space was non-Haken. A proof was obtained in 2009 using a
blend of theory and computation, and the details can be found in
the following paper:
<ul>
<li>B.B., J. Hyam Rubinstein and Stephan Tillmann,
<a href="http://arxiv.org/abs/0909.4625/"><i>The Weber-Seifert
dodecahedral space is non-Haken</i></a>,
Trans. Amer. Math. Soc. <b>364</b> (2012), no. 2, 911–932.</li>
</ul>
<p>
Because the proof involves computation, there is a fair amount of
supporting data, including the 23-tetrahedron triangulation of the
Weber-Seifert dodecahedral space and its 1751 standard vertex
normal surfaces. This is stored in a Regina data file, which you
can download here:
<ul>
<li><a href="files/weber-seifert.rga">Download weber-seifert.rga</a> (162 kb)
</ul>
<p>
<i><a href="#contents">(Back to top...)</a></i>
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