Census manifolds

Snappy comes with a large library of manifolds, which can be accessed individually through the Manifold and Triangulation constructors but also iterated through in the following groups.

class snappy.OrientableCuspedCensus

Iterator/Sequence for orientable manifolds in the SnapPea Cusped Census, which consists of such manifolds with at most 8 ideal tetrahedra.

>>> C = OrientableCuspedCensus()
>>> for M in C[:5]:   # Just the first 5 manifolds
...     print M, M.volume()
m003(0,0) 2.02988321282
m004(0,0) 2.02988321282
m006(0,0) 2.56897060094
m007(0,0) 2.56897060094
m009(0,0) 2.66674478345

Includes the eight tetrahedra manifolds tabulated by Morwen Thistlethwaite.

>>> C = OrientableCuspedCensus()
>>> for M in C[-3:]:    # Just the last 3 manifolds
...     print M, M.volume()
t12843(0,0)(0,0) 8.11953285128
t12844(0,0)(0,0) 8.11953285128
t12845(0,0)(0,0) 8.11953285128

class snappy.OrientableClosedCensus

Iterator/Sequence for orientable closed manifolds in the SnapPea Closed Census. It consists of 11,031 manifolds which are the Dehn fillings on cusped manifolds made from 7 ideal tetrahedra with a certain lower bound on the injectivity radius.

>>> C = OrientableClosedCensus()
>>> M = C[0]
>>> M.volume() # The smallest hyperbolic manifold!
0.942707362777

class snappy.AlternatingKnotExteriors

Iterator/Sequence for Alternating knot exteriors from the Hoste-Thistlethwaite tables. Goes through 16 crossings.

class snappy.NonalternatingKnotExteriors

Iterator/Sequence for nonAlternating knot exteriors from the Hoste-Thistlethwaite tables. Goes through 16 crossings.

class snappy.CensusKnots

Iterator/Sequence for knot exteriors in the SnapPea Census as tabulated by Callahan, Dean, Weeks, Champanerkar, Kofman and Patterson. These are the knot exteriors which can be triangulated by at most 7 ideal tetrahedra.

>>> K = CensusKnots()
>>> M = K[75]
>>> M
K7_4(0,0)
>>> M.volume()
3.635251186672
>>> Manifold('v0114').volume()
3.635251186672

class snappy.LinkExteriors

Census of links/knots using the classical numbering system of Tait/Conway/Rolfsen/Christy. Includes knots through 11 crossings, and links through 10 crossings. Mostly useful just for links as the Hoste-Thistlethwaite table of knots is much more extensive. Takes as argument the number of components.

>>> C = LinkExteriors(2)    # 2 component links
>>> len(C)
273
>>> C[20]
8^2_8(0,0)(0,0)
>>> for M in LinkExteriors(5):
...     print M, M.volume()
10^5_1(0,0)(0,0)(0,0)(0,0)(0,0) 14.6030607534
10^5_2(0,0)(0,0)(0,0)(0,0)(0,0) 12.8448530047
10^5_3(0,0)(0,0)(0,0)(0,0)(0,0) 10.1494160641

class snappy.MorwenLinks

Morwen Thistlethwaite’s table of links with at most 14 crossings (about 180k links). For instance, to look at first few 2-component links do:

>>> C = MorwenLinks(2)
>>> for M in C[:3]:
...     print M, M.volume()
... 
DT[ebbccdaeb](0,0)(0,0) 3.66386237671
DT[fbbdceafbd](0,0)(0,0) 5.3334895669
DT[fbccdefacb](0,0)(0,0) 4.05976642564

To look at those with 3 components and 11 crossings do:

>>> C = MorwenLinks(3, 11)
>>> len(C)   # How many such links are there?
329

class snappy.NonorientableCuspedCensus

Iterator/Sequence for nonorientable manifolds in the SnapPea Cusped Census. Contains such manifolds through 7 ideal tetrahedra.

class snappy.NonorientableClosedCensus

Iterator/Sequence for non-orientable closed manifolds in the SnapPea Closed Census. These are Dehn fillings on cusped manifolds with at most 7 tetrahedra.