Cusped hyperbolic 3-manifolds constructed from 8 ideal tetrahedra
cusped_8tet_o.txt : 12846 orientable manifolds
cusped_8tet_n.txt : 2998 non-orientable manifolds
The notation is essentially the same as Jeff Weeks's "terse triangulation"
format, but with slightly more redundancy.
Example:
haabaabbcacccadcabbdbbdedcbfbcdgddaeadchcddgbebhbecfcfagafdhdgcha_ajajaaaaaadpaaco
The initial "h" indicates "8 tetrahedra".
Each of the subsequent 16 blocks of 4 letters is read:
tet q face r is glued to tet s face t.
For example, "aaba" indicates that tet 0 face 0 is glued to tet 1 face 0.
The 16 letters after the underscore represent the corresponding gluing
permutations, coded by the letters a through x according to lexicographic order
of the standard numerical codes:
a = 0 1 2 3 (the identity permutation)
b = 0 1 3 2
c = 0 2 1 3
...........
w = 3 2 0 1
x = 3 2 1 0
Notes.
(1) A reasonable attempt was made to ensure completeness of these lists,
but as many steps were involved in the computations it is entirely possible
that there are omissions.
(2) The manifolds were distinguished using the canonical triangulation feature
of SnapPea, and the manifolds are arranged in order of complexity of their
canonical triangulations. Very occasionally, because of the limitations of
machine accuracy, SnapPea can mis-identify a triangulation as being canonical
(see Jeff's comments on this in the SnapPea source code); therefore it's possible
that there are duplications in the lists of manifolds.
(3) These manifolds have been incorporated into the Python version of SnapPea:
M. Culler, N. M. Dunfield, and J. R. Weeks. SnapPy, a computer program for
studying the geometry and topology of 3-manifolds, http://snappy.computop.org
Morwen Thistlethwaite October 2010