in SnapPea format
is provided below.
132 of these manifolds are hyperbolic (with geodesic boundary and/or toric cusps).
There are 298 combinatorially inequivalent orientation-reversing gluing patterns
for the faces of the octahedron,
available
here.
After subdivision of the octahedron into 4 tetrahedra they give rise
to 298
triangulations,
so our main task was to decide which of them
encode homeomorphic manifolds. We provide here the list
of all these 298 triangulations, that one may use to test the
effectiveness of a computer
program aimed at
distinguishing and
matching triangulated 3-manifolds.
We provide one separate list for each homeomorphism
type of the boundary:
empty (37 triangulations),
one torus (81 triangulations),
two tori (9 triangulations),
one genus-2 surface (113 triangulations),
one torus and one genus-2 surface (2 triangulations),
one genus-3 surface (56 triangulations; this file has a slightly different format
than the other ones, because it comes from a previous census).
The (non-user-friendly) Haskell code using which we have obtained
the above data is
here.
The matching of the triangulations was performed using
Orb
and later checked and complemented by theoretical work.
The result is the following list, subdivided according to the
topological type of the boundary and hyperbolicity.
The first column refers to one of the triangulation files
listed above and the second column is the position
(starting from 0) of the triangulation in this file:
Closed (17 manifolds, all non-hyperbolic),
One-cusped hyperbolic (9 manifolds),
One-cusped non hyperbolic (21 manifolds),
Two-cusped hyperbolic (2 manifolds),
Two-cusped non hyperbolic (5 manifolds),
Genus-2 boundary hyperbolic (63 manifolds),
Genus-2 boundary non hyperbolic (16 manifolds),
One-cusped and genus-2 boundary (2 manifolds, both hyperbolic),
Genus-3 boundary (56 manifolds, all hyperbolic;
this file has a slightly different format
than the other ones, because it comes from a previous census).
Page last updated on February 29, 2008