This folder contains a temporary collection of reference manifolds
for organizing the census.  Once I know what's going on I'll give
them permanent reference numbers.

The ONLY Chern-Simons value set by hand is CS(figure eight) = 0.
All others are derived from it.

Be sure to recheck all this information, as a lot of changes
have been made re orientations, etc., and there could be errors
here.  Also, write the SnapPea 2.0- basis changing module before
redoing this stuff.  In particular, some of the bases are
not the best (e.g. on tr4.1, cusps 0 and 3 don't agree).

tr4.3 may be eliminated, because it's a child of tr5.1.

ref num:		tr1.0
name:			figure eight
orientability:	orientable
num cusps:		1
cusp shape:		rectangular
volume:			2.0298832128193072
Chern-Simons:	0
homology:		Z
symmetry group:	D4
chirality:		amphicheiral
link notation:	L104001
Adams-Sherman:	AS1
parents:		tr2.0 (1.08... - i 1.72...)
children:		
mutants:		tr1.1 (half turn on embedded punctured torus)

ref num:		tr1.1
name:			figure eight sister
orientability:	orientable
num cusps:		1
cusp shape:		
volume:			2.0298832128193072
Chern-Simons:	1/4
homology:		Z/5 + Z
symmetry group:	Z/2 + Z/4
chirality:		amphicheiral
link notation:	N/A
Adams-Sherman:	N/A
parents:		tr2.0 (1.08... + i 1.72...)
				tr2.1 (0.86... - i 2.68...)
children:		
mutants:		tr1.0 (half turn on embedded punctured torus)
note:			There is a 3-fold ambiguity in choosing the shortest
				meridian for this manifold.  The ambiguity can be
				resolved in a natural way by defining this manifold
				as a (-3,1) Dehn filling on Whitehead left.geom.
				(Whitehead left.geom is Whitehead left with the
				shortest peripheral curves.)

ref num:		tr2.0
name:			Whitehead left.geom
orientability:	orientable
num cusps:		2
cusp shapes:	
volume:			3.6638623767088761
Chern-Simons:	-1/8
homology:		Z + Z
symmetry group:	D4
chirality:		chiral
link notation:	L205001
Adams-Sherman:	AS2
parents:		-tr3.0  (1.06... - i 2.23...)
				tr3.2   (2.12... + i 1.80...)
				tr3.3   (2.12... - i 1.80...)
children:		tr1.0   (3,1)(,)
				tr1.1   (-3,1)(,)
mutants:		tr2.1 (half turn on an immersed 3-punctured sphere)

ref num:		tr2.1
name:			Whitehead sister.geom
orientability:	orientable
num cusps:		2
cusp shapes:	Cusps are equivalent and square.
volume:			3.6638623767088761
Chern-Simons:	1/24
homology:		Z + Z
symmetry group:	D4
chirality:		chiral
link notation:	?
Adams-Sherman:	none
parents:		tr3.0   (0.96... + i 3.14...)
				-tr3.0  (1.06... + i 2.23...)
children:		tr1.1   (2,1)(,) or (-1,2)(,)
mutants:		tr2.0 (half turn on an immersed 3-punctured sphere)

ref num:		tr2.2
name:			
orientability:	orientable
num cusps:		2
cusp shapes:	Cusps are equivalent.  Cusp shape is rectangular,
				yet horoball packing is not mirror symmetric.
volume:			5.3334895668981196
Chern-Simons:	1/24
homology:		Z + Z
symmetry group:	Z/2 + Z/2 + Z/2
chirality:		chiral
link notation:	L206003
Adams-Sherman:	N/A
parents:		tr3.3  (1.26... + i 2.72...)
				tr3.5  (2.53... - i 0.83...)
children:		tr1.0  (0,1)(,)
mutants:		tr3.0 (half turn on embedded 3-punctured sphere)

ref num:		tr2.3
name:			
orientability:	orientable
num cusps:		2
cusp shapes:	Cusps are equivalent.
volume:			5.33348956689811959
Chern-Simons:	1/24
homology:		Z/3 + Z + Z
symmetry group:	Z/2 + Z/2 + Z/2
chirality:		chiral
link notation:	N/A
Adams-Sherman:	N/A
parents:		tr3.3   (1.26... + i 2.72...)
children:		
mutants:		

ref num:		tr2.4
name:			
orientability:	orientable
num cusps:		2
cusp shapes:	Cusps are not equivalent.
volume:			5.3334895668981196
Chern-Simons:	1/24
homology:		Z + Z
symmetry group:	Z/2
chirality:		chiral
link notation:	L209059
Adams-Sherman:	N/A
parents:		tr3.4  (1.26... + i 2.72...)
children:		
mutants:		

ref num:		tr2.5
name:			
orientability:	orientable
num cusps:		2
cusp shapes:	0 + 2i
				0 + 2i
				cusps are equivalent
volume:			7.32772475341775216
Chern-Simons:	0
homology:		Z2 + Z + Z
symmetry group:	Z2 + Z2 + Z2
chirality:		chiral
link notation:	
Adams-Sherman:	
parents:		
children:		
mutants:		

ref num:		tr3.0
name:			3-chain.geom
orientability:	orientable
num cusps:		3
cusp shapes:	
volume:			5.33348956689811958
Chern-Simons:	-5/24
homology:		Z + Z + Z
symmetry group:	D6
chirality:		chiral
link notation:	L306001
Adams-Sherman:	AS3
parents:		tr4.0   (1.26... + i 2.72...)
				tr4.2	(2.97... + i 2.48...) (inferred)
				tr4.4	(2.53... - i 0.83...) (inferred)
				
children:		-tr2.0  (-3,1)(,)(,)
				tr2.1   (-1,2)(,)(,)
				-tr2.1  (2,1)(,)(,)
mutants:		tr2.2 (half turn on embedded 3-punctured sphere)

ref num:		tr3.2
name:			Borromean rings
orientability:	orientable
num cusps:		3
cusp shapes:	
volume:			7.3277247534177521
Chern-Simons:	0
homology:		Z + Z + Z
symmetry group:	extended octahedral group
chirality:		amphicheiral
link notation:	L306002
Adams-Sherman:	N/A
parents:		tr4.3
children:		-tr2.0  (1,1)
				tr2.0   (1,-1)
mutants:		tr3.3 (half turn on an embedded 3-punctured sphere)

ref num:		tr3.3
name:			Borromean rings sister
orientability:	orientable
num cusps:		3
cusp shapes:	Cusps 1 and 2 are equivalent to each other,
				but not to cusp 0.
volume:			7.3277247534177521
Chern-Simons:	1/4
homology:		Z + Z + Z
symmetry group:	extended dihedral group <2,2,4>
chirality:		amphicheiral
link notation:	L308009
Adams-Sherman:	N/A
parents:		
children:		-tr2.2	(-1,2)(,)(,)
				tr2.2	(-2,1)(,)(,)
				-tr2.3	(2,1)(,)(,)
				tr2.3	(1,2)(,)(,)
				tr2.0   (,)(1,1)(,)
				-tr2.0  (,)(-1,1)(,)
mutants:		tr3.2 (half turn on an embedded 3-punctured sphere)

ref num:		tr3.4
name:			?
orientability:	orientable
num cusps:		3
cusp shapes:	The three cusps are pairwise inequivalent.
volume:			7.3277247534177521
Chern-Simons:	1/4
homology:		Z + Z + Z
symmetry group:	D2
chirality:		amphicheiral
link notation:	tr3.4(1,0)(1,0)(0,1) is a homotopy sphere,
				but I don't know how to draw the link.
				[Try a second half turn.]
Adams-Sherman:	N/A
parents:		
children:		-tr2.4  (2,1)(,)(,)
				tr2.4   (1,2)(,)(,)
				-tr2.3  (-1,2)(,)(,)
				tr2.3  	(-2,1)(,)(,)
mutants:		

ref num:		tr3.5
name:			
orientability:	orientable
num cusps:		3
cusp shapes:	cusp 0  0 + i 2 sqrt(3)
				cusp 1  0 + i   sqrt(3)
				cusp 2  0 + i   sqrt(3)
				Cusps 1 and 2 are equivalent by
				orientation-reversing symmetries.
volume:			10.1494160640965362
Chern-Simons:	0
homology:		Z + Z + Z
symmetry group:	D4
chirality:		amphicheiral
link notation:	
Adams-Sherman:	
parents:		four-cusp manifolds of volume 14.66...
children:		tr2.2  (,)(,)(0,1)
				-tr2.2 (,)(0,1)(,)
				two-cusp manifolds of volume 7.32...
mutants:		

ref num:		tr3.6  (NOT USED IN CENSUS PROGRAMS)
name:			
orientability:	orientable
num cusps:		3
cusp shapes:	1/2 + i sqrt(3)/2
				 0  + i sqrt(3)
				 0  + i sqrt(3)
				0;  1 = 2;
volume:			10.1494160640965362
Chern-Simons:	
homology:		Z2 + Z + Z + Z
symmetry group:	extended dihedral group <2,2,4>  (Z/2 X D4)
chirality:		amphicheiral
link notation:	
Adams-Sherman:	
parents:		
children:		
mutants:		

ref num:		tr3.7
name:			
orientability:	orientable
num cusps:		3
cusp shapes:	
volume:			10.1494160640965362
Chern-Simons:	1/4
homology:		Z + Z + Z
symmetry group:	D2
chirality:		amphicheiral
link notation:	
Adams-Sherman:	
parents:		
children:		
mutants:		

ref num:		tr4.0
name:			nonalternating 4-link chain
orientability:	orientable
num cusps:		4
cusp shapes:	All cusps are equivalent and square.
				All symmetries of horoball packing must extend
				to the whole manifold, to get the full 64 symmetries.
volume:			7.3277247534177521
Chern-Simons:	0
homology:		Z + Z + Z + Z
symmetry group:	nonabelian order 64
chirality:		amphicheiral
link notation:	L408002
Adams-Sherman:	AS4
parents:		tr5.0
				tr5.1 (4.24... + i 2.66...) (inferred)
children:		tr3.0  (1, 2)(,)(,)(,) or
					 (2,-1)(,)(,)(,) or
				-tr3.0 (1,-2)(,)(,)(,) or
					 (2, 1)(,)(,)(,) or
mutants:		

ref num:		4.1
name:			
orientability:	orientable
num cusps:		4
cusp shapes:	All cusps are equivalent.
				The shape is that of a hexagon lattice.
				The odd  numbered cusps are tangent, and
				the even numbered cusps are tangent, but
				no odd numbered cusp touches an even
				numbered one.
volume:			10.149416064096536
Chern-Simons:	0
homology:		Z + Z + Z + Z
symmetry group:	D3 x D4
chirality:		amphicheiral
link notation:	
Adams-Sherman:	
parents:		
children:		tr3.4   (1,1)(,)(,)(,)
						(-1,2)(,)(,)(,)
						(-2,1)(,)(,)(,)
mutants:		

ref num:		tr4.2
name:			
orientability:	orientable
num cusps:		4
cusp shapes:	Cusp 0 and 3 are equivalent, but no other pairs are.
				
volume:			10.149416064096536
Chern-Simons:	0
homology:		Z + Z + Z + Z
symmetry group:	Z/2 + Z/2 + Z/2
chirality:		amphicheiral
link notation:	
Adams-Sherman:	
parents:		tr5.2  (2.63... + i 3.14...)
children:		tr3.4   (1,1)(,)(,)(,)
				tr3.3   (-1,2)(,)(,)(,)
				tr3.4   (-2,1)(,)(,)(,)
				-tr3.0	(,)(1,1)(,)(,)
				tr3.0	(,)(-1,1)(,)(,)
mutants:		

ref num:		tr4.3
name:			
orientability:	orientable
num cusps:		4
cusp shapes:	Cusp 0 is distinct, but 1, 2 and 3 are equivalent.
				
volume:			10.9915871301266282
Chern-Simons:	-1/8
homology:		Z + Z + Z + Z
symmetry group:	D6
chirality:		chiral
link notation:	
Adams-Sherman:	N/A
parents:		
children:		-tr3.0	(-1,1)(,)(,)(,)
				tr3.2	(,)(1,1)(,)(,)
				tr3.3	(,)(-1,1)(,)(,)
mutants:		
note:			THIS MANIFOLD WON'T BE NEEDED IN FINAL
				SET BECAUSE IT'S A CHILD OF TR5.1.

ref num:		tr4.4
name:			
orientability:	orientable
num cusps:		4
cusp shapes:	0 + i sqrt(3)
				All cusps are equivalent.
volume:			10.149416064096536
Chern-Simons:	1/4
homology:		Z + Z + Z + Z
symmetry group:	extended dihedral group <2,2,4>
chirality:		chiral
link notation:	
Adams-Sherman:	
parents:		tr5.3
				tr5.4 
children:		tr3.0 (1,0)(,)(,)(,)
mutants:		

ref num:		tr4.5
name:			
orientability:	orientable
num cusps:		4
cusp shapes:	0 +  i
				0 +  i
				0 + 2i
				0 + 2i
				(0)(1)(2=3)
volume:			14.6554495068355043
Chern-Simons:	0
homology:		Z2 + Z + Z + Z + Z
symmetry group:	Z2 + Z2 + Z2 + Z2
chirality:		amphicheiral
link notation:	
Adams-Sherman:	
parents:		
children:		
mutants:		

ref num:		tr4.6
name:			
orientability:	orientable
num cusps:		4
cusp shapes:	 0  + 2i
				 0  + 2i
				1/2 + 3i
				 0  + 2i
				(0=1)(2)(3)
volume:			14.6554495068355042
Chern-Simons:	1/4
homology:		Z + Z + Z + Z
symmetry group:	D2
chirality:		amphicheiral
link notation:	
Adams-Sherman:	
parents:		
children:		
mutants:		

ref num:		
name:			tr5.0
orientability:	orientable
num cusps:		5
cusp shapes:	All cusps are equivalent.
volume:			10.14941606409653620
Chern-Simons:	1/4
homology:		Z + Z + Z + Z + Z
symmetry group:	Z/2 x a nonabelian group of order 120
				(probably Z/2 x S5, but I still need to check)
chirality:		amphicheiral
link notation:	
Adams-Sherman:	
parents:		
children:		
mutants:		

ref num:		tr5.1
name:			
orientability:	orientable
num cusps:		5
cusp shapes:	cusp 0     1/2 + i
				cusps 1-4  0 + 2i
				cusp 0 is distinct, but all other cusps
				are equivalent
volume:			14.6554495068355043
Chern-Simons:	0
homology:		Z + Z + Z + Z + Z
symmetry group:	a nonabelian group of order 32
chirality:		amphicheiral
link notation:	
Adams-Sherman:	
parents:		
children:		tr4.0 (0,1)(,)(,)(,)(,)
				tr4.0 (-1,1)(,)(,)(,)(,)
				tr4.3 (,)(1,1)(,)(,)(,)
				-tr4.3 (,)(-1,1)(,)(,)(,)
mutants:		

ref num:		tr5.2
name:			
orientability:	orientable
num cusps:		5
cusp shapes:	1/2 + i
				2i
				i
				i
				i
				0; 1; 2; 3 = 4
volume:			14.655449506835504
Chern-Simons:	1/4
homology:		Z + Z + Z + Z + Z
symmetry group:	Z2 + Z2 + Z2
chirality:		amphicheiral
link notation:	
Adams-Sherman:	
parents:		
children:		tr4.0	(0,1)(,)(,)(,)(,)
				tr4.0	(-1,1)(,)(,)(,)(,)
				tr4.2	(,)(,)(1,1)(,)(,)
				tr4.2	(,)(,)(-1,1)(,)(,)
				tr4.2	(,)(,)(,)(1,1)(,)
				tr4.2	(,)(,)(,)(-1,1)(,)
mutants:		

ref num:		tr5.3
name:			
orientability:	orientable
num cusps:		5
cusp shapes:	i
				2i
				i
				i
				2i
				0 = 3; 1 = 4; 2
volume:			14.655449506835504
Chern-Simons:	0
homology:		Z + Z + Z + Z + Z
symmetry group:	Z2 + Z2 + Z2 + Z2
chirality:		amphicheiral
link notation:	
Adams-Sherman:	
parents:		
children:		tr4.0  (1,0)(,)(,)(,)(,)
				tr4.0  (0,1)(,)(,)(,)(,)
				tr4.2  (,)(0,1)(,)(,)(,)
				-tr4.4 (,)(,)(1,1)(,)(,)
				tr4.4  (,)(,)(-1,1)(,)(,)
mutants:		

ref num:		tr5.4
name:			
orientability:	orientable
num cusps:		5
cusp shapes:	0:     i  (but no 1/4 turns in sym grp)
				1-4:  2i
				0; 1 = 2 = 3 = 4
volume:			14.6554495068355043
Chern-Simons:	0
homology:		Z + Z + Z + Z + Z
symmetry group:	a nonabelian group of order 32
chirality:		amphicheiral
link notation:	
Adams-Sherman:	
parents:		
children:		 tr4.4 (1,1)(,)(,)(,)(,)
				-tr4.4 (-1,1)(,)(,)(,)(,)
mutants:		

ref num:		tr6.0
name:			
orientability:	orientable
num cusps:		6
cusp shapes:	All six cusps are equivalent.
volume:			14.65544950683550429
Chern-Simons:	0
homology:		Z + Z + Z + Z + Z + Z
symmetry group:	D4 x octahedral group
chirality:		amphicheiral
link notation:	
Adams-Sherman:	
parents:		
children:		
mutants:		

ref num:		tr6.1
name:			
orientability:	orientable
num cusps:		6
cusp shapes:	
volume:			19.7968546183154821
Chern-Simons:	0.17757106691993692
homology:		Z + Z + Z + Z + Z + Z
symmetry group:	D2
chirality:		chiral
link notation:	
Adams-Sherman:	
parents:		
children:		
mutants:		

ref num:		tr6.2
name:			
orientability:	orientable
num cusps:		6
cusp shapes:	
volume:			19.7968546183154821
Chern-Simons:	0.1775710669199369
homology:		Z + Z + Z + Z + Z + Z
symmetry group:	D2
chirality:		chiral
link notation:	
Adams-Sherman:	
parents:		
children:		
mutants:		

ref num:		tr6.3
name:			
orientability:	orientable
num cusps:		6
cusp shapes:	
volume:			19.7968546183154821
Chern-Simons:	0.0724289330800631
homology:		Z + Z + Z + Z + Z + Z
symmetry group:	D2
chirality:		chiral
link notation:	
Adams-Sherman:	
parents:		
children:		
mutants:		

ref num:		tr7.0
name:			
orientability:	orientable
num cusps:		
cusp shapes:	
volume:			19.7968546183154821
Chern-Simons:	0.1775710669199369
homology:		
symmetry group:	D14
chirality:		chiral
link notation:	
Adams-Sherman:	
parents:		
children:		
mutants:		

ref num:		tr7.1
name:			
orientability:	orientable
num cusps:		
cusp shapes:	
volume:			
Chern-Simons:	
homology:		
symmetry group:	
chirality:		
link notation:	
Adams-Sherman:	
parents:		
children:		
mutants:		

ref num:		tr8.0
name:			
orientability:	orientable
num cusps:		
cusp shapes:	
volume:			24.0921840801887553
Chern-Simons:	
homology:		
symmetry group:	nonabelian order 64
chirality:		amphicheiral
link notation:	
Adams-Sherman:	
parents:		
children:		
mutants:		

ref num:		
name:			
orientability:	orientable
num cusps:		
cusp shapes:	
volume:			
Chern-Simons:	
homology:		
symmetry group:	
chirality:		
link notation:	
Adams-Sherman:	
parents:		
children:		
mutants:		
